Re: should you ever lay down QQ preflop?
 

I've folded kings preflop before and didn't regret it. It gets to a point that if the stacks are so ridiculously deep and they're just jamming on you and it's so close to being -EV that it's barely worth it that I'd just rather fold, depending on how you deep you are in the tournament and/or what the tournament is. When I folded KK it was in the monthly $500 tournament on stars and there were 4 raises preflop and I had to call off over 100 bb's.

Re: should you ever lay down QQ preflop?
 

Meh it depends on the stacks and reads and table dynamics, there's not nearly enough of that info included here to comment on this particular situation, but yeah I can think of a few spots off the top of my head where I either folded QQ or called only for set value. There are plenty of players whose reraising range is like QQ+ and AK, particularly if you raise from EP and they reraise from like MP.