Hey

1. Preflop you have 125 bbs, limper has 61 bbs. I would 3x the limp or even 3.5x instead of just min raising due to being so deep. If we get a nice flop like you did you want to be playing a bigger pot and getting more value out of your hand. As well if you only min raise to iso the limper the button,sb,and bb may assume everyone will call the min raise therefore you end up playing 4-5 handed a lot of the time which may be difficult. The big blind in this hand is usually going to call no matter what in a $5 tourney so minimum you are going to play a 3 handed pot by min raise iso'ing the limper because the limper is most likely a fish and is never folding to a raise anyway.

2. As played half pot c-bet is fine as we do not want to drive players with weaker pairs/draws out of the hand with your hand strength and potential.

3. Player in the big blind is going to check/raise a lot of two pairs, sets, and 45 gets there as well. The majority of the time he does not put you on a flush draw since you iso'd pre, c-bet the flop, then double barreled turn and are representing a strong top pair/overpair, therefore he can also bluff the flush as well. I like the call on the turn, but when you call on the turn the plan should be to call the river unless the board pairs for a possible full house or another spade comes which may let him improve. When you call the turn you are doing it to get max value on the river and you have to assume you have the best hand, therefore if river is a blank and nothing changes. EASY CALL. If he has a better flush its a cooler. AsQs and AsKs he would probably 3bet preflop being so deep so they are unlikely. So the only hands that could beat you are KsQs and AsXs. And 4s5s of course.