Yes on basically all counts.
I think it's pretty standard to 3bet like 3x the open when IP and maybe 4x OOP. So it this case I make it $.90 - $1. I mean if he's a drooler and will call larger, fine, but against an unknown I like 3x the open amount.
So you bet the flop because you want him to fold worse hands (small pp)?
Since you're not betting for value (to be called by worse) and you're not betting as a bluff because he never folds anything better, it seems like a pretty bad bet to me.
Even if he does call the flop bet with say QQ, do you really think he continues calling on the turn? Once the Ace hits you basically have a 1 street hand against most opponents. So if he checks flop/turn you bet the river. If he bets the turn you call and generally fold to a 2nd bet on the river unless he's a chronic bluffer.
Go read this thread,
WA/WB, it's all explained there.