Regarding the first thing, you know how Saiyans in Dragon Ball Z get stronger every time they nearly die? Allen kind of works like that, too. The harder he gets his ass kicked, the more buff he gets when he heals. It’s not guaranteed given the whole plot beat is show-original, but it’s likely this is where they’re going with it and they’re using it to set up future Allen stuff: Allen is fixing to come back unbelievably fucking jacked out of nowhere, and the comic doesn’t really explain it very well, so this is probably extra connective tissue they’re adding to make that work better.
Regarding the mole thing… he’s almost definitely not actually the mole. The Viltrumites do not like him very much, to put it very, very mildly.
Nope. Homeboy grew that. That’s an actual beard.
Being able to rip out your beard in one single grab, with no blood or pain, leaving the mustache intact, is honest to God a Viltrumite superpower. That’s part of their power set. It’s called the Toolock Pull.