I find they are good for training the mind to "this button to escape, this one to nuke" mindset, but the difficulty is laughable. I have not come close to losing since my 10th game or so, even with new champs.

I find 3v3 alot harder than 5v5. Play ai SR for training then go into blind pick

Keep playing. The best thing you should do is report them to tribunal and they will see a ban sooner or later.
OR, you can do what I do which is act unnaturally nice when they try to flame me
Examples:

[Flamer]: usuk maokai
[Me]: Thank you for that really awesome constructive criticism. It should help me win a team fight.

[Flamer]: **** YOU
[Me]: I <3 you too

To the OP, i feel you. When i first started, I've experienced the very same thing you're going through. What i recommend is to jump in and play 5v5. 3v3 will not do much in terms of improving your skill, as the game play is totally different. Play any champ you like and disregard other's opinions about whether you can play that champ or not. After all, like you mentioned, you purchased the champ therefore you have the right to play it. The more you play, the better you will get. Try to communicate with your team mates and explain to them your situation. I'm sure you'll eventually meet someone who will be kind enough to show you the ropes. Good luck.

There is so much more to track in a 5v5 game. 3v3 seems simple by comparison. I don't even know what champs are AD/AP/Carry/Mid/Jungle/Top/Bot with any great accuracy. I know if I play riven they tell me to go top all the time and I do. If I play Cait they tell me to go bottom. I'm ok with that. When to hit dragon, baron, stealing buffs, ganking, counter jungling, and stuff like that I am just beginning to understand from watching vids and endless reading. It kind of makes my head hurt.

I know a ton of people have already said this but keep playing. I honestly go through a lot of my games not saying a thing besides maybe a "glhf" and "mia" etc etc. That's really all there is to communicating. If someone is raging at you and you think its getting to you ignore him and keep calling the mia and etc. The information gets across but you can't hear what they are saying which is prob just negative things anyway. Regardless, its a matter of practice, in 2 or so years I have played over 900 summoner rift games and probably around 100 ranrked games and I am still nowhere near close to being "good." I have friends that play half as many games as I do and I still feel they are better players than I am but this game is about practice and experience which you can only do if you just dive into it and play.

However, there are some other ways of getting better at the game and improving your chances of winning SR. Primarily learning how to farm. Farming is more common in SR than TT and Dominion. This can be done numerous ways probably the most common being to just to start a custom game sit in a lane and last hit. At the 10 minute mark check how much CS you were able to get. I think ideally you want to try and hit 70 and I think the max is around 100. The more farmed you are the better your items which means you should be stronger than your opponent. This will put you in a more favorable position to win team fights and small skirmishes. Hope this helps

If it helps, I play SR exclusively, and have no idea what the TT meta is, what kind of champ goes where or does what, how the jungle works, how the altars or whatever they're called works, when to go for the spider, etc. etc.

It's not that there's more to know - it's just that it's different. If you play it, you'll get used to it. Hell, it's actually easier to transition from TT to SR then vice versa, because there are so many more resources for learning - the featured spectator games, the vast majority of streamers, all the professional tournaments, are all SR.

Just watch and learn, and then transfer that to blind normals, and go from there

As a top laner you are essentially on an island it is noy attypical for you to stay up there for 20 minutes and farm as long as you call mia and as long as you are pushing their tower whenever your opponent top is ganking another lane. Counter jungling is essentially keeping an eye on your jungler and seeing if they are going into enemy jungle. If they do and they get attacked by an enemy jungler be prepared to help or ping for someone closer to go help them. Other than that counter jungling is the jungler's job but how successful is up to your lanes. Any other lane you will have to learn these objectives which I will do my best to sum up for you.

The golem buffs respawn ever 5 minutes. Assuming their jungler is starting blue and clears relatively fast.
Blue buff 2 min, 7:10, 12:30, 18:00
Red buff 3:30, 8:30, 13:30, 19:00
These are all very rough estimates since all champions have different clear times and whether or not the jungler ganks but buffs play an extremely important role especially early-mid game. This is because it can cover some champions weaknesses. Let's take Anivia for example, strong burst but very mana dependent, blue buff covers that weakness. Therefore its typical that Anivia will go grab blue buff around 7:30. However, if you deny Anivia that blue some people may be able to eploit that weakness or difference in strength. As a result you can expect certain champs to be at certain places just by when buffs are up. This is extremely important information.

Dragon respawns every 6 minutes. Begin warding dragon pit around 8-10 minute mark and be sure to refresh the ward there. Basically whenever the enemy team is out of position you want to rush baron. Example, there are 3 people top including their jungler, that is when you should ping baron and have your mid, bot and jungle take dragon. You will keep up in gold and experience as a result. Then add 6 minutes to the current time and type it in chat. Then you can see when the next dragon will spawn. Since the gold is significant there will be a lot of fights that happen here so always be prepared to fight there.

Baron respawns every 7 minutes first spawning at the 15 minute mark. This is a task that you should only do if you are confident you can do it fast with taking minimal damage. It's not worth it if you finish off baron and then get aced. Usually this is done late game where members of the team have a lot of items already but need the buff.

Sorry for wall of text but its a lot of information. Just keep track of the time and expect fights to break out around then so always be prepared for a fight especially around those times.

Doesn't matter how many games you play any time you lose your team mates will get mad and rage, at you possibly aswell. Grow a thick skin and don't worry what others say about you or your play.

It isn't that I cry myself to sleep or anything, it just takes the fun out of the game. I rage at my screen sometimes but I don't feel the need to type the things I'm yelling in chat.

Anyway I just have a hard time getting my head around the seemingly omnipresent mentality of "Make no mistakes, but don't practice in games I am playing because I don't want your sorry butt on my team."

Ah well. I have gotten better with Kayle, still tweaking her build and I still mis ults all the time but I'm working on it. People just frustrate the hell out of me sometimes.