Does he already know that he is a half tiger not just a mask man?

I don't think so

Not forgetting the tail. He keeps saying "His tail move a lot" as if that's totally normal LOL

Yeah. I have been thinking (and Hyuuga san has thought it a few times himself), that our adorable Host is not necessarily the BRIGHTEST bulb in the pack. The sweeetest? Yes. Just not the brightest. Only him and the one stalker girl from the club honestly believe it is a mask.