castling to king side

what are the advantages of making this move?

Absolutely none.

Just makes it harder to centralise your king in the endgame.

You should castle to move your king to the side of the board where it's safer and to connect your rooks.

@1

"what are the advantages of making this move?"

1. Your king is safer on the g-file than on the e-file
2. Your rooks are connected and ready to become active
3. You gain 2 tempi: you play like 3 good moves Kf2, Rf1, Kg1 for the price of 1 move

It depends. In some positions, 0-0 might lose you the game. I'd recommend keeping your options open to both castling kingside and queenside rather than trying to castle as soon as humanly possible. That being said, if the attack is only down the center, castling kingside is slightly better than castling queenside. However, if the center is already open and castling queenside would bring a rook to the attack, that might be better.