Early levels Aatrox just farms under turret and pokes with E. It sounds underwhelming but in a battle of longevity he will win. Currently Hecarim and Irelia buttfuck him after they get their items but Aatrox can push them around early like most other champions. Against Fiora, you want her to engage onto you in your minion wave and knock her up. She's vulnerable to poke before she gets lifesteal.
Riven, Swain and Pantheon can buttfuck him at any stage of the game but what champion doesn't have counters? Lissandra and Kennan are just going to poke and disengage until they get a zhonyas and then they will murder you. You can poke them out early. If you can force Jax to build vamp sceptar or delay his TF or sheen/phage combo you can counterall in him if you have ignite advantage/full bloodwell. If he rushes sheen and phage then you can poke him out and force his tp.
If gnar rushes bork you lost the lane but they have a bork gnar so just farm up for teamfights. If he rushes phage you can outpoke him but if you miss your q you're dead. If Gnar goes sunfire cape you have to poke him down. Your E does magic damage so it shouldnt be so bad. If you can get a good engage onto mega-gnar take it. Mind the skillshots.
Sion and Mao are free farm. Sion will push you around force you under turret so you can farm safely. They can both setup ganks for their jungler easy so that's something to keep in mind.
As for his PBE buffs its nice though most Aatrox players can keep their bloodwell full as is. It will definitely help in situations where you get bursted/cc'd before you can ult. It's a boon but it should not affect his general performance but instead help him secure those "close" kills.
Also fizz is a bitch.