need help on (failed) all-in calls against draws

I'm a new poster and relatively new player so please excuse any "dumb" stuff.
Twice yesterday I busted out of tourneys early on very similar situations and I don't know if I played them right or anywhere close to right. Both involve an all suited flop.
First one_early in SnG, I'm middle position and get 5,5. Blinds are 10,15 and I raise it to 65 all fold to BB who calls. Flop is 5,6,7 spades he checks, I bet pot and he raises me the same amount which I call. turn is 3h which he checks, I bet, and he raises all in. The mistake I assume is I call it and he shows As,7 and a spade comes on the river to beat me.

Second one, multi table early on I get Q,Q in middle position and raise 4xBB, all fold to SB who calls. Flop 3 low clubs, he checks, I bet 2x pot, he reraises all in and I call (dumb?) he shows Ah,5c and turn is club, I lose.

Now my main questions are, was I an idiot to call the huge bets on the all suited flop? As it turns out I was correct that they didn't have the flush and in my limited understanding of odds, at the flop in both cases I was the (clear) favorite. So the other question, were they right to push in those situations or was it a poor play on their parts? (It was early on so we were close in stack size). I am frustrated because I was all in as the favorite (which I know you still lose plenty of just hurt because it was back to back tourneys) but do I have to fold that anyway?

Sorry if any pertinent info is missing and thanks in advance for any feedback.