Do grandmasters trade queens?
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Also, do they trade pieces in general? Where they sacrifice one piece for the capture of the same type of piece?
Yes, grandmasters trade queens and other pieces all the time.
They trade whenever there is some advantage in doing so.
Here for example is a queen trade on move 8 in a World Championship Match:
https://www.chessgames.com/perl/chessgame?gid=1252043
Fischer never had any badly placed pieces: he traded them.