100nl standard cbet & double barrel Q

Progress in poker is about refining the basics. I'm going over my basics again.

PokerStars No-Limit Hold'em, $1.00 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver Cards)

BB ($99.50)
UTG ($71.70)
Hero ($93.50)
CO ($130.05)
Button ($186.25)
SB ($103.55)

Preflop: Hero is MP with http://www.flopturnriver.com/phpBB2/.../smiles/jc.gif, http://www.flopturnriver.com/phpBB2/.../smiles/qh.gif.
1 fold, Hero raises to $4, 1 fold, Button calls $4, 2 folds.

Flop: ($9.50) http://www.flopturnriver.com/phpBB2/.../smiles/2s.gif, http://www.flopturnriver.com/phpBB2/.../smiles/kh.gif, http://www.flopturnriver.com/phpBB2/.../smiles/3d.gif (2 players)
Hero bets $7, Button calls $7.

Turn: ($23.50) http://www.flopturnriver.com/phpBB2/.../smiles/td.gif (2 players)
Hero bets $15

Do we cbet this flop, and why?

Do we double barrel our picked up draw, and why?

I like it, you're probably not going to fold out small pairs with just one shell and you've picked up a lot of equity here.

C/r AI has merits too but seems very spewy.