Assassin's are supposed to use the whole kit to burst someone (Kata need the whole q + e + r to kill and sometimes even W before ult, Zed has to use his shadow to deal enough damage to kill you unless you're pretty low, Kassadin can't 100-0 you so he needs to use his kit to come in and out of the fight constantly, Talon needs to R, E, AA, Q, AA, W, AA to kill you most times so he even needs a lot of AA to actually kill you most of the times, and these are oly 3 of the examples I can give), fizz can kill you with 2 skills and still have the strongest ass-saver skill in the whole game (the damn pole) so: no, he's in a perfect spot and doesn't need any buff, even if his damage might be a bit low (don't know since it's been a while since I fought him) he's still incredibly strong, the meta is an ADC meta, so assassins and those who counter both assassins and ADC are incredibly strong and valuable that's why fizz might feel a little weaker than past season, but that's just a feeling.
Now commenting your changes:
E: Fizz's e should be used EITHER as an escape OR as a dive, he shouldn't be allowed to just fuck up but still kill you AND get e back to escape, since to die as fizz (unless you find some hard counters, and yes, fizz is getting "bad scores" snce his coutner are more played this pre-season) you need to screw up big times.
R: That's the most broken skill league ever heard, almost as broken as: press q to insta win the game... no coutnerplay, a kill every time he's got ult and also, with the E change, no way to die since you will ALWAYS have the reset on E and escape to safety (maybe killing that ungler who's ganking you to help his lane), so a BIG no.
I know that when the meta shifts and your main gets hard countered it sucks, but you can't ask for bs buffs that alone would need fizz to deal damage to himself rather than the enemy just to balance them out (and I don't mean hp costs, but actually hitting yourself rather than the enemy).