I know that, according to chess rules, every move should be made with a single hand. However, this does not clarify if, when making an en passant capture, I should move my pawn first or remove the opponent's pawn from the board. I understand that the result is pretty identical in both cases, but I wonder what is the preferred consequence if you are playing an international tournament game with strict rules, for example. So, for instance, what do most grandmasters etc. generally do first? (Moving their own pawn vs. removing the enemy pawn.)
Both methods are legal. There is, however, one difference between the two options. If the en passant turns out to be illegal, then you must make a move involving the first piece you touched, if it is legal to so.
So, if you touch the opponent's pawn first, you must capture the opponent's pawn. If you touch your own pawn first, you must move your own pawn.
I can't say I know which is preferred by grandmasters. But it seems like moving your own pawn first is somewhat less likely to result in disaster if the move turns out to be illegal-imagine having to capture a defended pawn with your queen.
According to FIDE rules of chess
3.1 ...If a piece moves to a square occupied by an opponent’s piece the latter is captured and removed from the chessboard as part of the same move...
So you move your piece (pawn is a piece as per rule 2.2) in order to capture the opponent's piece.
What is en passant?
According to the rule 3.7 d. it is a sort of capture
A pawn attacking a square crossed by an opponent’s pawn which has advanced two squares in one move from its original square may capture this opponent’s pawn as though the latter had been moved only one square.
This capture is only legal on the move following this advance and is called an ‘en passant’ capture.
Think of this: you need to move your own piece first if you play online in order to capture opponent's piece.
Second part of your question regarding how grandmasters, etc do it. Obviously, can't speak for the whole community, however it is considered unethical and in full violation of the rules to remove opponents piece first and then 'forget' to move your own piece (this tactics is often used by hustlers). All chess players must follow the official rules.