Should I Kill Morkvarg?

You can either choose to convince him or fight him now. If you convince him, he'll make one request: kill Morkvarg once you lift the curse. Regardless how you go about the conversation (or fight) you'll still be able to get the cursed fang off of him.

What happens if you don't kill Morkvarg?

Nothing happens, you never meet up with him again. He doesn't have any effect on other NPC's, except the shop dealer who gives you an additional little bonus. This page here tells you everything about Morkvarg and the quest.

Is Morkvarg good or bad?

Morkvarg is considered one of the most evil and brutal men from Skellige. Ten years prior to the events of the game, he and his crew pillaged and raped coastal villages around Skellige, even those belonging to his own clan.