Just want a little confirmation and advice on the ladies.

Sunday Millions today. QQ second hand on the button. Just me and the BB after I raised preflop. Flop is 10 9 4 rainbow. He checks, I raised and he went all in. I folded. Bad move?

Live MTT week ago Tuesday. Final table. I have qq in BB. Both of us have almost same average table stacks. I'm ahead maybe 5k. Button raises 3x. I call and we're heads up. Flop hits 9s 10s Jh. I bet half the pot. He reraises. I look at the guy and tell him he doesn't have aces and he doesn't kings but I think he has 14 outs and I think I can win without this hand. He was pot committed and had shoved everytime he was. I'd played with him the entire tournament. He told me he'd show his hand if I'd show mine. I showed him the ladies and he showed me As Ks. Would you have moved all in knowing you guessed his hand? Should I have checked the flop, called his smaller raise (which I'm pretty sure he'd put my raise in at that spot), or moved all in on the flop?

Bet sizing would be nice for the first hand. Have the HH?

Second hand I guess it's how much you have behind and if you feel you have an edge. I probably get it in because I don't know how to fold but that's me

At the live MTT, you were a dog despite having the made hand. Still, depending on how much was in the pot already (you didn't say bet sizes), it probably would have been correct for both of you to put all the money in if you knew each other's hands.

The first hand, you can make a case for folding provided your reads indicate villain doesn't make this play as a bluff... though there's also a case to make that a player ahead here wouldn't shove that flop and that this is a bluff, especially if you've portrayed a tight image. It's hard to see AA/KK flat pre, but I can see TT, 99 or 44 flatting and hoping for the set. Maybe an OESD crai's that flop. Maybe he's bluffing. Again, with the right read or if this play came out of nowhere, I can see a fold here, though otherwise I would call and make him show me the nuts.

But you are typically well ahead in the 2nd. Not only do you have the overpair, but you're sitting on an OESD as well. What could villain have that completely crushes you, and what are the odds villain would shove the flop if he had you beat like that? Wouldn't he try and milk you for chips instead? And when he agreed to show if you mucked, that should have set off alarm bells. That usually indicates a bluff, at any level.

I'm usually calling both, although

1) depends on stack sizes, and exactly what pot odds you are getting. You could easily be ahead, he could be semi bluffing QJ/J8 kinda hands, maybe valuing JJ/AT/KT. You have resuck outs vs T9 and a set isn't too many hand combinations to worry about.
For all of these though , stack sizes/pot odds on the call are very important. Maybe reads too.

2) depends on your edge/how much you are willing to gambol. I don't think I've folded QQ on JT9 to 1 player for a long time.