Considering I have the nut blocker sould I jam this spot considering Villains stats?

PokerStars - $0.25 PL Hi (6 max) - Omaha Hi - 5 players
Hand converted by PokerTracker 4: http://www.pokertracker.com

UTG: 77.48 BB (VPIP: 37.48, PFR: 23.78, 3Bet Preflop: 11.18, Hands: 733)
CO: 68.24 BB (VPIP: 64.81, PFR: 11.11, 3Bet Preflop: 4.17, Hands: 57)
Hero (BTN): 132.52 BB
SB: 238.8 BB (VPIP: 32.11, PFR: 19.58, 3Bet Preflop: 4.32, Hands: 386)
BB: 246.12 BB (VPIP: 19.14, PFR: 8.58, 3Bet Preflop: 3.03, Hands: 611)

SB posts SB 0.4 BB, BB posts BB 1 BB, CO posts penalty blind 1.4 BB

Pre Flop: (pot: 2.8 BB) Hero has 4d 5c Kh Ks
fold, CO checks, Hero raises to 4.8 BB, fold, BB calls 3.8 BB, CO calls 3.8 BB

Flop : (15.2 BB, 3 players) 2h Ts 7h
BB checks, CO checks, Hero checks

Turn : (15.2 BB, 3 players) Ah
BB bets 11.64 BB, fold, Hero calls 11.64 BB

River : (38.48 BB, 2 players) 8d
BB bets 29.44 BB

Pre, I like the play especially with the dead money and position. I am c-betting that flop after you took the initiative pre and raised. Your hand needs protection and you are getting value. Turn is eh. After checking flop BB can reasonably assume you don't have nut hearts. As you played I guess I'm just folding turn. Since you called turn I guess you have to shove river as idk why else you're calling turn other than to bluff it off on non-pair rivers.

As played, I think I'm shoving river with his stats.

I checked back just because I know I'm getting called by alot of draws and I didn't want to bloat the pot if draw card gets there or get x/r and get blown off my hand. But after the Ah comes I feel like it's the only way to win the pot is to call t/shove river. I just wanted to know if it's ok to call turn or should I just give it up? Or if I bet flop and get called or x/r, should I continue with the same play if I get called and x/turn or give it up if I get x/r?

Sometimes its best to just surrender the 4.8bbs you have invested instead of losing a stack. That's why I'd probably be folding turn after you checked flop (giving up). Personally I think that's the best way to play this turn as played pre and on the flop. I usually wouldn't be calling turn with the intention of bluffing river. You have near 0 equity in the hand and calling with just blockers with the intention of bluffing is usually not the best play imo.

This.

Bolded for emphasis. It's really bad. You shouldn't try to win every single pot. When you have 0% equity, you should fold.

Bluffing river seems really bad. He looks like he has a flush and you don't since you checked flop. Also because the Ah is out there but I doubt this is of concern to people at this level.