A bishop like that is a fianchetto, the knight doesn't always have to go there.
You can look at openings like the king's indian defense, king's indian attack, pirc, and catalan.
It's also possible on the queenside like the Larsen's, Owen's, and queen's indian defense.
But also, fianchettos can happen in all sorts of openings.
I suppose some basic considerations are... you usually want to preserve the bishop since it influences the center (and even the opponent's side of the board) from a very safe place. If your opponent has it, then sometimes it's good to force a trade by getting a bishop to h3 (pinning it to the rook). To prevent this happening to you, you can move the rook so there is no pin.
Another consideration is when the knight is blocking the bishop like that, then it eventually wants to move out of the way. If the bishop is supporting a knight in the center, then that can be fine, but in your picture (knight on f3) it wants to move, usually early in the middlegame.
As for king safety, the king is generally very safe. One idea to attack it is to push the h pawn down the board to open lines. To prevent lines from opening the side with the finachetto can push their h pawn 1 or 2 squares forwards.
I want to study the basic theory behind it but I don't know what to google lol