Would a professional level player put their queen in danger of capture from the opposing queen with protection? Every now and then I will move my queen into a position that puts it in position to be captured by the opposing queen. Sometimes my opponents takes it and I capture their queen immediately. Also, sometimes they don't take it and neither of use loses a queen. 

Is it ever smart, except for obvious occasions, to lose your queen just to take the opposing sides queen?
You're referring to a queen trade, and yes, there're plenty of situations in which you want to trade queens. In general, trading queens simplifies the position, which is good if:


You're up material. The fewer pieces there are on the board, the harder it is for the opponent to cook up counterplay.
You're on the defensive. The fewer pieces there are on the board, the harder it is to launch a successful attack on the enemy king.
You have some kind of advantage that makes you win the endgame, e.g. fewer pawn islands (this is a technical chess concept that measures on how many separated pawns you have), an outside passed pawn, and so on.
Various other reasons (there are a ton of them).


Here's an example from the recent game Topalov-Maxime Vachier Lagrave.

1kr5/1r3p2/2np3p/p5p1/2P3P1/PPNq4/K1R3QP/7B w - - 0 39


Black has just played Qe3-d3, and it's White's turn. It should be clear that Black's queen is much stronger than White's right now: it's much more aggressively positioned and it's generating a lot of threats. So Topalov played 39. Qd2, offering the trade. MVL promptly played 39...Qxd2, because if he didn't, White would play Qxd6+, eating a pawn for free. 

This kind of exchange happens all the time at top level.