to answer the question, fold to the raise on the turn i think.

i think folding to the re-raise pre-flop OOP is better...

Agree with Muzz with regards to checking turn and calling if you have the right odds... 9 outs for nut flush but id be reluctant to add any for A on the river, given the way villain played the hand AK? although you did mention range to be quite high so unsure..

Im not very good though... just my thoughts