[GiantBuddha]

The title kind of says it all to me.
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Live 1/2 Fancy Play with AA

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Almost never a good idea.

That said:

I like that you have position on reraiser.
I don't like that your first raise was so small and his reraise was similarly small.
I don't like the third guy in the pot who's always calling once you call.
I do like the relatively shallow stacks. If you were ~$300 deep I think this would be terrible.

So in answer to your questions:

* Did I pick a good spot for this play?
not really, but it's not the worst spot to get cute
* How's my range for BB preflop?
sounds about right, but I wouldn't rule out AK or AQs even if you've seen him flat call it before. He's in a good squeeze spot this particular hand
* What's up with the $20 c-bet?
got me. that's a horrible bet no matter what he has. typical confused $1/2, though.
* How does flop action affect the range for BB?
I think it's less likely he has JJ given the tiny c-bet, and absurd for him to have AKo at this point
* Is a call on the end correct? I can't fold after the way I played preflop, can I?
You're getting better than 3:1. You wanted to underrep your hand and you have. Hopefully it worked and he has QQ or KK. I think you win more than 25% here, but it's close, considering MP is probably drawing to beat you and most of his money's in the pot already. And that's why I don't really like preflop.