As stupid as this sounds-- I don't know how to bet when I have the nuts.

I was going to post in NL HH's but thought that this was so basic that I wouldn't get any responses.

HAND 1:
No read on the villain.
Villain's weak flop/turn betting is either a good thing or very bad (or I'm more of a fish than I'd like to think). Some will say to lead out or bet the flop but I didn't want to give this guy a chance to play back at me. I think I have to fold to a raise.

River betting to you all is probably elementary, but I was not very sure what to do at that point and am curious if my river bet was appropriate. I considered pushing, but thought that gave away my hand and gave him too good of a chance to get away cheap. If he's been betting the naked As draw he at least has to call a near pot bet and if he's careless he'll put me all in, hoping I had QsQ/AA/AK.

Party Poker No-Limit Hold'em, $ BB (10 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

MP2 ($26.80)
MP3 ($39.57)
CO ($26.95)
Button ($24.40)
SB ($23.80)
BB ($25.90)
UTG ($49.90)
Hero ($25.90)
UTG+2 ($12.80)
MP1 ($18.70)

Preflop: Hero is UTG+1 with K, K. SB posts a blind of $0.10.
1 fold, Hero raises to $1, UTG+2 calls $1, 3 folds, CO calls $1, Button calls $1, 2 folds.

Flop: ($4.35) 4, J, 8 (4 players)
Hero checks, UTG+2 checks, CO checks, Button bets $1, Hero calls $1, UTG+2 folds, CO folds.

Turn: ($6.35) J (2 players)
Hero checks, Button bets $2, Hero calls $2.

River: ($10.35) K (2 players)
Hero bets $9, Button calls $20.40 (All-In), Hero calls $11.40.

Final Pot: $51.15

HAND 2:

I think I muffed this one badly. I raised to pot but don't know if that was right since it was minbet early with so many cold callers. I probably don't get called regardless of my raise (and I must raise, correct?), but wanted some opinions. Since the board's rainbow, would a raise to $.75 or $1 be better?

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

MP2 ($22.05)
Hero ($22.63)
CO ($25.86)
Button ($7.63)
SB ($27.38)
BB ($18.40)
UTG ($3.65)
UTG+1 ($33.33)
MP1 ($14.85)

Preflop: Hero is MP3 with 8, 7. SB posts a blind of $0.10.
1 fold, UTG+1 calls $0.25, 1 fold, MP2 calls $0.25, Hero calls $0.25, 1 fold, Button calls $0.25, SB (poster) completes, BB checks.

Flop: ($1.50) 5, 6, 4 (6 players)
SB bets $0.25, BB calls $0.25, UTG+1 calls $0.25, MP2 folds, Hero raises to $2.25, Button folds, SB folds, BB folds, UTG+1 folds.

Final Pot: $4.50