Should I Kill Gaetan?

If you're looking for the objectively best choice in terms of loot, we recommend sparing Gaetan. You'll gain 200 experience and be granted a new quest called Take What You Want. This will lead you to a stash of goods near Keira Metz' cabin, defended by some bandits.

What happens if I kill Karadin?

so it looks like either way if you spare/kill karadin you can open up dialogue with lambert and play gwent with him. If you kill him and loot his body you get 2 demetrium bombs and 2 GrapeShot bombs.

Should I kill the Witcher with Lambert?

You can choose either to spare Karadin or help Lambert kill him. Lambert will be angry with Geralt if you insist on leaving Karadin, but there will be no real consequences to the quest as it will not impact Geralt's future interacations with Lambert. Regardless of the choice, the two will go on their separate ways.