First off, congratz on your first post. If you really want to learn poker, you have come to the right place.

The problem with your post is that we have no context for the hand. Next time whenever you are confused in a spot, I would recommend posting a hand with reads etc.

As for this particular spot though, raise the QQ because players do love alot of hands worse than QQ that you can get value from. Limping QQ can be a disaster because with multiple people going to the flop if an A or a K comes off you are very likely to not have the best hand. Also, lots of people in the pot highly increases the chance that someone will make a hand better than QQ.

The biggest thing here is that QQ is one of the best hands in poker, and when you have one of the best hands in poker you want there to be money in the pot.

As far as getting 3 bet, its very difficult to answer this question without more reads, but in general if the player seems loose you can 4b for value, or if the player seems extremely tight you can just fold. I wouldnt advocate flatting 3bets OOP very often at all.