Queen exchange

Sadly there are very few chess rules which we can say are 'Always' correct. It would depend on your personal preference (and that of your opponent) whether you or they like/dislike playing with queen's off the board, and details of the rest of the position. But in general yes - castling is often beneficial for king safety so stopping your opponent from doing so can mean his king is less safe... Though also consider that with the queen's off the board there are fewer threats to the king so it might not be as crucial that the king is well sheltered. Depends on the rest of the pieces and details of the position

@1

"Is it always correct to exchange the queens so that the opponent is unable to castle?"
++ No. After queens are exchanged castling is less important and a king is often better in the center with the endgame approaching. Examples:
https://www.chessgames.com/perl/chessgame?gid=1044389

https://www.chessgames.com/perl/chessgame?gid=1258181 

https://www.chessgames.com/perl/chessgame?gid=1252048 

A lot of the time, the advantage of trading queens so your opponent cannot castle is to inhibit their development as well as the safety of the king - it will take a few extra moves to consolidate. Your opponent is fine, but it makes everything a little bit harder for them.