Yi and Kata are fairly squishy champions, so if you do get caught as either of them, it's very likely for them to burst you down.
In terms of Yi, it's generally best that you don't initiate fights, as that isn't what Yi specializes in. Yi specializes in dealing damage, especially after most of the enemies blow their CC or ultimates on the tanks and initiators. Once the initiators have initiated teamfights, this is where you are relatively safe to go in. Either wait for enemy CC to die down or wait until your team CCs the enemy team. This is fairly similar with Katarina.
Xin Zhao on the other hand can be an initiator since his ultimate provides damage immunity to ranged attacks from outside the circular barrier after you cast your ultimate. However, at this stage if you're working on not dying, you may want to save your ultimate for peeling or purely for the CC/knockback.
If you are unable to do damage, check your builds, make sure they're in line with whatever champion you're playing and learn to build according to specific games. You're level 20 which I'd say is a perfect time to build for specific occasions, perhaps the enemy team is very auto attack oriented, or maybe they are very magic damage heavy. If you are unable to buy such items, you may be lacking on CS (or minion kills) or other forms of gold income such as jungle camps. Since you don't seem to play support, generally you would want to keep your CS to as much as you can without bothering your teammates as much.
Seek out guides and techniques on YouTube or other websites such as LoLking or Mobafire.
Hopefully this gives you a good start!
Good luck out there!