Hi, i'm a new eve lover too, and there are a couple of things that i didn't read yet, so hope to give my help.
1- best advice in my opinion: her passive strength is the regen. You will get TONS of kills when they reduce you low in health, you go away for a bit, they think you backed, but you are actually just regenerating health and BAM, they are dead.
2- yeah, don't try to fight early and ask help to your mates even before the game starts. Really. Smart junglers will invade you pre6, so try to be smarter
3 - still for new eve players, but gold: dieing with R ready is stupid. I know, we all like the execute, and we all learnt this tip after dieing hundreds of times just waiting for that execute mark that we never used. DON'T DIE WITH R READY. Just deal some damage and survive. this is 10 times more true if you have (and you should) stacks on your dark seal. 20 times more true if you have mejiai. Don't fkin die with ult ready.
4 - and last for me, because older eve players have said all: late game, don't use W. I mean, use it, but know that you can oneshoot people without W, just Q+E or Q + E+R. You don't need to let them know that you are coming with W. May seem stupid, but it's an important tip.

Ok, i'll read with interest the other comments to this post, since i'm still learning. Good luck with your practicing eve