Playing Nintendo Switch for two?

Can you play in pairs with the Nintendo switch if everyone removes a controller from the switch? Or do you have to buy a controller again to play in pairs?

The Joy-Cons can be used as independent controllers, so yes.

But that's not really comfortable.

You can use the two joycons on the side of the switch for 2 players.

That depends on the games. Mario Kart or Mario Party, i.e. Games that are designed for local multiplayer, also work if everyone uses a Joy Con.