Tristana is primarily a late game hero. She can get kills early in the game, but it requires well timed aggressive play with the rocket jump burst damage, explosive shot and possibly ignite. Its kind of hard to give tips for in a general sense though because it really depends who you are facing for weather or not you can do that. That being said you dont want to max explosive shot because you will need to have rapid fire maxed around 13-14 at a minimum for when you are a strong physical attacker. Most of her kills come late game in team fights when she can chew people apart.
Mundo, Mord, Chogath and Alistar can all be hard champions to get kills with because of their skillsets. Alistar stuns and knocks people back into his team so they can kill someone. Mord is mainly a tank, who can contribute some damage to a fight, but lacks big damage or stuns and slows to get kills. Chogath can get kills with his ultimate or with his burst damage from his spells, but that primarily comes in team fights, you cant really solo people down by yourself. Mundo can be a bit more of a killer because of cleavers snare, however he provides some decent sustained damage, but not huge burst damage, or extremely high consistant damage which makes getting final hits on champions more difficult. As far as feeling squishy on tanks, they take items to feel more durable. Early on in games they are still pretty squishy. Its not until you get a bunch of items that they are really beefy and hard to take down.
Warwick is an excellent ganker and you should be able to get some kills on him. His ultimate provides a nice stun and some solid damage for him and his team to chew people apart. With him you should always be looking for opponents that have overextended and you can go kill with some of your friends. As far as losing to the other warwick, its very possible that you guys ranked up different skills and his were better for a toe to toe encounter.
Ezreal is a very strong killer. He is best used as attack damage at the moment. Because of his blink and long range attacks he is very good at chasing and taking people down.
Honestly I think you just need to play the game a bit more. As you play more you will become better accustomed to situations where you can go in and kill people, and others where you cannot.
If you really want to get kills, the easiest way is to start off with some dps casters. Someone like annie has very high burst damage to where you put a lot of burst on someone being attacked and kill them off. That might be a good starting point. Another good choice can be stealth champions like twitch and shaco because you can sneak up on people when they aren't suspecting you, allowing you and your teammates to kill them.
As for general tips, always look for people to gank. If someone pushes themselves out to far you can ping the target and get some of your teammates to come with you to kill the target. If you play to passive or dont look for these opportunities, you lose some of the largest places to get kills.
Another very useful thing is summoner abilties. Ghost in particular will help you chase down low HP targets and finish them off. It can also be used to help you escape. Using these at the right time often results in either you staying alive or other people getting killed.
As for something like teamfights, if you are a squishy champion like annie you have to be very careful of your positioning. You ideally want to attack a squishy target that you and your team can quickly destroy, however you have to be very careful not to overextend and get yourself killed. If you get killed constantly early in teamfights, you obviously aren't going to kill many people.
Something which I have mentioned before and I cant emphasize enough, you really have to look for people to kill, and think up ways to get them killed. Remember they are always trying to stay alive just like you are, so you have to find ways to catch them offguard. Attacking unsuspecting opponents is always the best way to kill them.
Lastly use your team. Its very hard to just run off by yourself and kill people. You have to work with your team to do so. When you coordinate with them you wont get every kill as there are several people there, but you will certainly get more. Ontop of that you will become stronger, the enemy will become weaker than you which in turn will make it easier to kill them in the future.
Running off to gank someone by yourself will often not be enough and they will be able to escape, or they will have teammates come help and you can get killed. If you have a couple friends with you then that target will die much faster and have a very hard time getting away. This also goes for laning periods in games. If the enemy only things they are fighting against the people in their lane they will feel safer. If you pop up suddenly the numbers are against them and you have a much better chance of scoring a kill.
You may want to try to AT with someone who can help out. There are several players here in the new player forum that have threads that are willing to play with new players. Sometimes, just playing a few games where someone else takes the lead will give you insight on when to engage and when to back off.
This is also an excellent suggestion. Just like going to school its much easier to have some guidance when learning things instead of having to teach yourself. Having someone beside you to offer some guidance can make a big difference.
Hopefully some of this will help a bit. If you have any more questions or need more tips dont hesitate to ask.