Villain was 44/33/15 over 44 hands.

AF was 5. Hadn't seen him fold to c-bets yet. He's positionally aware and likes stealing/protecting his own blinds, probably knows my CO range is fairly wide.

I know the flop bet size is fine(could be potsized), but should I be calling his turn raise? I'm not 100% sure he's floating on this board. and I'm also not too sure wether he's gonna raise his turned flush here..doubt it.
Checked the river as I was pretty sure he was gonna bet his entire range here, so I went for c/shove instead of a value bet.

Anyways, as played, do we call, shove or fold his turn raise?

If called, do we shove river or bet a little less to get more weaker hands to call? I'm guessing most flushes, trips etc, won't fold and air folds anyway, so a shove is right?

No-Limit Hold'em, $0.20 BB (5 handed) - Hold'em Manager Converter Tool from FlopTurnRiver.com

SB ($20.67)
BB ($11)
UTG ($20)
Hero (MP) ($35.31)
Button ($65.52)

Preflop: Hero is MP with 7, 8
1 fold, Hero bets $0.60, Button calls $0.60, 2 folds

Flop: ($1.50) 7, A, 8 (2 players)
Hero bets $1.30, Button calls $1.30

Turn: ($4.10) K (2 players)
Hero bets $2.70, Button raises $6.40, Hero calls $3.70

River: ($16.90) 8 (2 players)
Hero checks, Button bets $9.80, Hero raises $27.01 (All-In), 1 fold

Total pot: $36.50