How to beat Teemo with Jax?

Hello yes I am a noob who wants to play Jax but I have 3 problems.

First I am consistently either camped or against a double top lane, so I am 0/11 by midgame consistently. I stand back and they kill me with range or a pincer from behind the turret.

Secondly enemy top laners constantly duel me, meaning I die to such a degree I have 80-ish farm by 20 minutes. I try to hop to a ward but I'm always out of them because I need to ward the river. The minion wave is never inbound so I can't jump to that, and I can't jump to turrets.

Third I have nothing to kill Teemo. My Counter doesn't work against his autos because they count as spells. I can't kill him early because I need my Q and W to do that, and by then he either has his blind or his movement buff so I can't keep up with him. I can't kill him late because I have no CC outside of my counter that has the effective range of my AAs and has a very short duration.

How do I deal with any or all of these.