Hey. I'm fairly new to the game and I main Ahri and somewhat Ashe. I have a few questions:
1) Ahri's build: Is having both Rod of Ages and Rylai's okay? Sometimes I find my self to have more health than our actual tanks at late game with this build....
2) Ashe's build: Should I be rushing an IE? I usually start with Statikk Shiv and Runnan's, but while it helps me clear waves at the speed of light, I feel like I'm not doing enough damadge. Should I be rushing IE and Bloodthirster instead?
3) Master Yi: How the eff do I counter him?? As Ahri, I love interrupting others' ults, and I have no trouble escaping from Yi usually, but it's his Alpha Strike harrasse that I'm worried about... He always out-sustains me... As Ashe, I am hopeless against him because his ult makes him un-flippin'-slowable and renders me compeletly at his mercy...And it seems if there's a Yi on the opposing team, he WILL come find me and kill me. How the eff do I counter him??
4) Is Quinn supposed to go mid?
5) When would be a good time for me to get blue buff as Ahri?
6) What should I do if I have a buff from killing someone that I don't need? (like Red as Sona or some crackpot thing like that)
7) Assists: I've been getting shizloads of assists as Ashe, and I know that can't be a good thing... How should I get more kills and stop making my support go on killing sprees and rampages?
8) Should the ADC ward?
9) AP mids ward, right?
10) As I hit level 23, I'm beginning to see a lot of super aggressive plays, (like 3 people homeplate diving for one kill... that they didn't get) Should I also start to be as aggressive as I can in mid? I usually try to prioritize turrets before kills, but that makes mid usually the 0/0/0 lane before late/mid game ganks...
Yeah... if you actually read and decide to answer that, I LOVE YOU!!

you can't counter yi. The only way to counter yi is to have stuns AND sustain.

Most of your questions can be answered with "it depends". I'll try to be more specific about when they're good or bad ideas though.

1) Building high health on Ahri might be a good idea when you're taking a lot of guaranteed damage; for example, against a very fed Karthus, it's impossible to avoid taking a lot of damage in teamfights from his ultimate. In most cases, Ahri's mobility is enough to keep her safe in teamfights. Zhonya's Hourglass is often a strong defensive item for situations where she'd require it, since it's harder to prevent autoattacks from AD Carries in lategame teamfights if your team is going on their backline, and you can use the clicky between cooldowns to win duels or survive while your team obliterates someone on you.

2. Avoid building Runaan's. It's extremely situational, and you should probably only consider it as a 6th item in very specific circumstances (needing to slow/kite multiple people for your team in the very late game, for example). A conventional start for most AD carries is 1 or 2 doran's blades early, possibly an early vampiric scepter, then either Bloodthirster or Infinity Edge. IE has more synergy with Ashe than BT due to her passive, but BT can be stronger if you need the sustain in teamfights. Static Shiv is very strong on her if you need wave clear (for defending turrets or pushing aggressively, like against split push comps), Phantom Dancer is stronger single target damage.

3. Stay away when you only have 3 minions and farm. He's extremely strong early and mid game, worthless late game as AP Yi, since he's entirely dependent on getting resets in teamfights. Once people are tanky in the lategame, he can't do anything. For Ashe it's trickier. Blade of the Ruined King is a good option because it makes it a lot easier to kite him - you can't slow him, but you can make yourself a lot faster. It'll often come down to your positioning (being too far back for him to alpha strike to unless he runs through your entire team, and hopefully they murder the hell out of him if he tries), and using your ultimate to disengage.

4. She can. People aren't entirely sure what to do with her yet. She's most conventionally played as an AD carry bottom with a support, but a lot of people have experimented with her in different lanes and roles.

5. The second blue buff is often donated from the jungler, around 7 minutes when it respawns if they started at blue, around 8 minutes if they started at red. If you don't have a jungler, whenever you can solo it safely without losing a massive amount of farm. I might wait for a while, like maybe around level 9-11 or so, depending on build.

6. Cackle and autoattack people to proc it. Red buff isn't bad on a support with a ranged autoattack, it just means it becomes a small peel in teamfights rather than a threat to the enemy carries.

7. Build more damage. I think this is more a consequence of you building static shiv and runaan's hurricane early. More single-target damage makes it far easier to get kills.

8. Sometimes yeah. Ideally other people ward for you, but you can't farm areas safely if they're unwarded, and you can't push for some objectives without wards. If that means you have to ward, then just do it. Carrying a pink specifically to do baron or dragon can often be a great idea if no one else thought of it.

9. Yes. It becomes pretty much a necessity to see when you can fight the enemy mid without dying to the jungler, and so that you can notify other lanes when your lane opponent roams. You often have the option of pushing aggressively or trying to follow them, and either can be valid options depending on how safe the lane they're roaming to will be.

10. Most people go aggressive in lower level play because it's fun, easy to remember when it pays off, and easy to blame your teams and forget about it when it doesn't. Mindless aggression is sort of the hallmark of bronze and silver play - people just going for kills when they can, and not knowing or caring if it'll backfire from having zero clue where the enemy jungler is, if the other person's build and summoner spells will mean they'll win, etc. The higher you go, the more people calculate about when their aggression is a good idea; going aggressive when they see the enemy jungler reveal himself elsewhere on the map, tracking enemy summoner spells, knowing at what level who is stronger and with what items, etc. Going aggressive is great if you'll win.

I'm short on time but let's see how far I can get before I have to leave.

1. At your level, anything that works is fine. However, Ahri has lots of mobility, so generally you shouldn't need to have that much HP.
2. You should never rush runaan's. Runaans is reliant on AD to be effective, and if it's your first item, it's going to be a terrible loss of money early on. Statikk is okay, but I wouldn't rush that either. Your best choice, if you want to rush something, is either IE or BT. definitely IE if you are behind, because you deal more damage with those crits, and you don't have to worry about losing stacks (which is the case for BT)
3. A good Master Yi is nearly unbeatable in the laning phase (I'm assuming he's AP). Stuns prevent him from doing anything for a time, but you really need your whole team to shut him down. Most Master Yis will build straight damage (aka "glass cannon"), and so if you can get your team to stun and focus him, he should melt in about 2 seconds or less. (Make sure you can interrupt his heal).
4. Quinn is an ADC, so usually she goes bot, but everyone knows she is not very good at the ADC role, so many higher level players send her top. There used to be a time when the meta called for ADC mids, so she can really go anywhere she wants, especially at your level.
5. Anytime you feel you have the time to. Early on I generally don't get it unless my jungler is there to help me.
6. There usually isn't a champion that absolutely doesn't need a buff. Maybe if you're Xerath and you got a red buff, sure, that's pretty useless. But other than that you can always fit a basic attack into your combo for red, and 20% cooldown is always nice. The important thing is that you took it away form the enemy, who probably got it because they needed it.
7. If all the kills are close calls, then don't worry about who gets the kills, but if the kill is certain, the support should generally stop attacking to give you the kill.
8. Everyone should ward. Think about it like this. Do I want to spend 3x75=225 gold to keep myself safe or risk 300+150=450 gold for the enemy team?
9. yes.
10. If you can zone them out, yes.

1) Rod of Ages probably isn't that great for Ahri. There are not many champions that you'd build it on. You're giving up a lot of mid game power while you're building RoA, and it doesn't pay off until later.

2) This is a strange concept for someone who is fairly new, but "clearing waves at the speed of light" is not something to itemize for on a ranged AD carry. Runaan's Hurricane is a very niche item. You should usually finish IE or Bloodthirster before finishing Shiv, and you really shouldn't be buying Hurricane at all.

3) The counter to AD Yi is having an organized team. He is completely dependent upon getting into range and lifestealing to stay alive. As you said, Ashe can't kite him with slows. You need a team that will make it hard for him to get close to you. Stuns, knockups, knockbacks, snares, etc. If he builds glass cannon offense with lifesteal, you'll never be able to solo him or outrun him but you should be able to melt him easily while your team holds him down.

4) Quinn is usually bot lane as an adc with a support, or solo top.

5) If you have a jungler, they get the first blue at 1:55 and sometimes the second one at 7:00. If they're not giving you blue buff after that, you should ask them. If you don't have a jungler, you should try getting it when you are comfortable with your ability to solo it, and only if you have pushed your lane out.

6) You can't really control which buffs you get from kills. All you can do is try to make use of it while you have it (and try not to die and give it away).

7) Just try; there's no real secret to this. Even though it is good when kills go to the adc, you should not prioritize getting the kill over winning the fight. For example, if it's 3v3 and a nearly-dead enemy backs away, it might not be good to focus on finishing them off if your teammates still need help with the other two enemies.

8) Outside of pro games, I don't often see ADCs picking up wards during the laning phase. But it's good if everyone on the team can pick up a ward here and there when having vision across the whole map becomes important.

9) Yes. Ward in either side bush or by the enemy wraiths.

10) This really depends on what champion you are and what champion you're up against. For some champions, that's their only real strength. They're not great at farming and not great at teamfights, so they have to make laning a living hell (dying hell?) for their opponent with aggressive plays.

1) It's an opportunity cost. Sorc shoes and Deathcap are a given. From there, your AP items can give health (Rylai's, RoA), armor (Hourglass), MR & CDR (Unholy Grali), Spell Pen (Void Staff), and some other options. Buying one means leaving other options behind.

2) I don't ADC much, but you will want some amount of early Lifesteal. Usually Bloodthirster or Vampiric + IE.

3) To deal with Master Yi, you will need hard CC, like a stun or charm. Ashe (and ADCs in general) will struggle with him, which is why ADC should share a lane with a CC-heavy support like Lulu, Thresh, Leona, etc. Ashe does have the Ult Arrow, but it won't stun him for long.

4) Quinn was supposed to be a utility heavy ADC, like Ashe. Mostly, I've been disappointed by her. Considering 3) above, her lack of CC makes a solo lane risky.

5) It depends on how much your jungler needs blue. Usually mid will get the second (~7:05) or third (~12:30) respawn. If you have no jungler, you will need to wait until you drive your lane opponent back to base without suffering heavy damage yourself.

6) You may want to harass your lane opponent with basic attacks more, but I mostly ignore it if it isn't useful.

7) Assists are still good money, and you should be getting most of your cash from last-hitting minions. I find the Beserker Greaves (upgraded boots) help in grabbing that killing blow.

8) Mostly, the support should ward, but you should get a ward or two if you have leftover money when shopping. It helps a lot early game (when the support is struggling to buy Sightstone and Philo) and late game (when pushing a lane, ward the jungle as you go).

9) If you don't want to die, solo lanes should definitely ward.

10) 20 cs is roughly the cash of 1 kill, and one turret is roughly 2 kills (750g for the team). Thus, you can just drive them from the lane repeatedly, go 0/0/0, and still dominate your lane. If you want to get more aggressive as mid, learn when it's safe to push the lane, then go gank top or bot.

I used the Build RoA on Ahri. But now its not really cost efficient. It may give you lots of health and mana to spam. But its not really going to help you. try something more bursty like DFG. It will help more. Only buy RoA if you are taking too much damage and need sustain.

1. RoA is a pretty late game build, makes your mid weaker so late is better.. not sure whether too since I'm not an ahri player. Judging from above I think you should skip it for something else.

2. DO NOT RUSH ATTACK SPEED ON ANY ADC, It's like never a good idea. Get an IE and vamp scepter for Ashe.

4. Quinn... usually he goes bot or top, but I think he can work since his ult gives mad ganking power with his E too. This is all theoretical but I think he will be popular in mid soon.

5. Usually Junglers will give it to you when it respawns about 7 mins, first blue is the Junglers.. anytime above that is yours pretty much (unless the jungler actually says dont take it)

6. Well it could help you dominate the lane more, but not much I guess? Try making plays if you can since you got a slow.

7. Getting alot of assists is pretty fine, you should get the kills if you can but an assist is also fine. (Better than letting the enemy go away)

8 and 9. Everybody wards. Period. Supports just buys more than usual.

10. Go with your playstyle, if you prefer farming till lategame (with the correct champs ofc, not with Lee Sin etc...) then do that.