Wow, this one is ugly....I'll give it my best shot.

FLOP: I dont see anything wrong with your play here.

TURN: Given the flop action and the turned spade, I really dont like raising here, since you would never want to be 3 bet. I would just call at this point knowing that if the villain is ahead of me with two pair, I have many outs to beat him, and I can draw cheaply. If the villain has a set its not the end of the world either since you will have 6 outs unless he has pocket kings with a spade.

Given that you raised the turn, I think you have enough to call the 3 bet. Youre too likely to have outs and be drawing live to consider folding IMO. Plus theres always that small chance your hand is still best.

RIVER: I understand your thinking but I dont like your play here. Since you have no read on the villain there is no way you can assume he will fold a better hand than you in this heads up situation even on that horrible board. Making this kind of play on the river without a read will be costly IMO.
So on the river, its between calling and folding IMO.

An argument for calling would go something like this, the pot is large and there are still 2 combinations of AK left without a spade, and there are 6 combinations with KJ left without a spade, and the villain may of played these hands in this manner on every street, I dont know the villain so maybe hes crazy enough to play QJ without a spade also. People are known to get overaggressive in these Blind vs Blind battles. I think i'll invest one more BB and call this river, even if I lose I can still gain some kind of information on the villain, which is important since we may be in a few more blind battles today.

An argument for folding would be, the villain has showed a tremendous amount of strength the entire hand, I have let him know repeatedly that I like my hand and he doesnt care. He 3 bet me on the turn on that very scray board, and then he bet the river on an even scarier board, I strongly believe the villain can beat one pair, theres no way my hand is good here 1/15 times so im folding.

I really dont think it matters in the long run whether you call this river or fold. So I would probably call and gain some information on the villain.