It’s a real beard, his mustache is just too powerful to be ripped out and needed a disguise

They say love is a battlefield and Kregg is a frontline commander

No, in the comic he killed them effortlessly and sustained no damage, in the show my assumption is that he was diverting suspicion by being there but also visibly injured. Since he’s far and away the strongest on Earth and everyone knows it it sells that he tried to help them against a superior threat and failed.

Sending people to horny jail?

I think the lore is that they altered their biology to siphon energy from another dimension to give them all their powers, before that they were basically humans. In the show Mark’s blood is explicitly radiation proof so I highly doubt a lightsaber would do much to their skin