Yeah, in hand 1 I just checked and then he checked. What then? Check again or bet?

Hand 2 I just didn't know how to play it regarding the player already all in. Played that really badly by checking and the folding. Terrible!

While we are on the topic of my dodgy KK play, here is a hand from today.

Party Poker No-Limit Hold'em, $0.50 BB (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

saw flop|saw showdown

MP2 ($36.55)
MP3 ($52.20)
CO ($57)
Button ($9.75)
SB ($34.61)
BB ($35.52)
UTG ($26.04)
UTG+1 ($96.73)
Hero ($45.50)

Preflop: Hero is MP1 with K, K.
UTG calls $0.50, UTG+1 raises to $2, Hero raises to $6, 6 folds, UTG folds, UTG+1 raises to $20, Hero calls $14.

Flop: ($41.25) 5, 4, 5 (2 players)
UTG+1 bets $26, Hero ??

Villain is a regular with 15/8/3 stats. His 4 bet surely means AA doesn't it? How many others hands would he have done that with? I called the raise hoping to hit a king or an ace which would help me maybe get away from it. I really hate calling on the flop to be honest. How would you guys have played it?