[tolbiny]

"Pre-flop you have two overcards, but not a pair. And they're not suited. So other than having overcards, you are playing a drawing hand."

With two limpers in AQo is generally going to be the best hand preflop- usually the only had that is currently better would be a samll pair wich is only a samll favorite. Meanwhile you are a big favorite over all other Aces (assuming that AK raises), all other Queens and all other hands you are moderate- small favorites over.
If your hand is likely to be best- then all the other hands are trying to outdraw you.
This is an easy value raise from the sb in this generic situation.

"Then Button calls. I'm putting Button on a made straight and BB on a made flush"

you are far to fidgid here, people play badly. Not only that but BB should be betting plenty of hands here that aren't a flush. Two pair, a set, a straight. Folding this turn in an enourmous pot for one bet is a mistake. A very large mistake.

"I would bet and I would also re-raise"

Yikes. The four flush is so obvious that there is no way i am three betting a raise here. I might consider check riaising, but i think its best to bet out as you have 2 potential callers and it is very easy for them to check through when the 4 card flush hits.

"He's not afraid of that king or that queen. At this point I put him on hand with either KX or QX, or maybe high suited connectors like JT. Then Button 3-bets. Now, he could have either KK, QQ, or KQ. But if he did, then he would have raised pre-flop. But if he had JTo then it would have been right for him to just call pre-flop and 3-bet a floped straight. At this point I start thinking hard about folding. When BB caps after you called the raise, I think it's time to swallow your pride and fold"

Folding with two back to you on the flop is likely the correct play. But once you call you should not fold for one more, at this point you are getting 20-1 almost enough just for a BD flush draw. Plus you have a BD straigh draw and your A and Q could be outs still.

"But like I said, I'm a fish."

No worries, stick around here long enough and you won't be.