Flopped full house please critique

[Rah]

Bet the flop, call the raise, checkraise the turn. You missed a bet. Also, unless villain is kinda LAGish, I see no point in three-betting the river. You have made it pretty clear that you have at least three of a kind. Villain raising means that he is not afraid of straight/flush, indicating that he holds KK. The whole hand is consistent with AK or KK, the raise on river leaning against KK.

[aK13]

I'd definitely bet this flop, as button is very likely to raise with anything and trap the player in the middle.

I also check/raise the turn. If he leads the river after my cap, I call and expect KK.

EDIT: I guess he can't lead the river, bet/call.