I really want to learn Evelynn & Alistar.

Not an Eve main myself, but I do play her a bit. Basically just farm, look for a lane even slightly pushed(maybe to the middle?) and then go in with your laners from behind since they can't see you and just spam Q. If you're going to die by someone and you're faster than them, or at least as fast, just kite them and spam Q, does a fuckload of damage. And personally I hate the idea of building Spell Vamp on Eve... maybe the lifesteal and AP-AD is good on Hextech Gunblade but I think there are much better choices.

Alistar's actually a pretty fun champion, if you can work with his ulti. Max q/w first (the heal from e isn't entirely useful, but a point in it early game helps nonetheless). Use flash/pulverise to set up plays, and use headbutt to push outnumbered/weakened foes towards you or if you're outnumbered to push them away from you. Oh, and if your team wants to tower dive make sure you go in first. That ulti makes them rather easy to do, even if you only have 7-8 seconds of it.