You should bet the turn - Of course he can have the Ac but on the BB, he can call with a large range of hands. I think that you can bet the turn for value.

On the river, I think that your call is correct. In 2NL, when they bet too small like that, it usually means they have a very good hand but I think you are ahead with your second flush.

You played this hand well, except that you didn't bet the turn.