Hi,
If you're going to bet the flop just pot it, otherwise just check/calling is fine.
As played pot the turn as well, clearly for value this time.
As played on the river hard to say, I very much doubt he's taking that line with Qx and for him to play a busted flushdraw this way after you bet both turn and river strong like that is rather unlikely as well. If you think the sum of that happens more than around 20% of the time pot odds dictates it's a call, otherwise it's a fold. I'll tell you right now if he's a reg it's a fold. If you have no idea it's fine either way it's never a big mistake.
Hope it helps.