NL2, 6-max, KK vs river min-raise

Pacific Poker - $0.02 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BB: 100 BB (VPIP: 21.83, PFR: 18.31, 3Bet Preflop: 9.43, Hands: 143)
UTG: 69.5 BB (VPIP: 21.05, PFR: 12.28, 3Bet Preflop: 5.26, Hands: 59)
MP: 183.5 BB (VPIP: 20.63, PFR: 7.54, 3Bet Preflop: 1.04, Hands: 257)
Hero (CO): 211 BB
BTN: 63 BB (VPIP: 40.82, PFR: 8.16, 3Bet Preflop: 5.17, Hands: 150)
SB: 194 BB (VPIP: 33.74, PFR: 17.28, 3Bet Preflop: 7.45, Hands: 753)

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has K♦ K♠

fold, fold, Hero raises to 3 BB, BTN calls 3 BB, fold, fold

Flop: (7.5 BB, 2 players) 3♠ J♠ 4♣
Hero bets 4.5 BB, BTN calls 4.5 BB

Turn: (16.5 BB, 2 players) 8♠
Hero bets 10.5 BB, BTN calls 10.5 BB

River: (37.5 BB, 2 players) 4♦
Hero bets 18.5 BB, BTN raises to 37 BB, fold,

What I am wondering here are about these two things:

• 1. Should I have bet the turn? I am OOP against a fish and the third spade comes, but this doesn't mean that he has a flush every time. However, if he doesn't, he might get scared and fold.
  
• 2. Is the river fold correct?