Sherlock: Is Moriarty alive?

I say yes. Sherlock faked his death rather cleverly

yes

I don't think so. I think Moffat and Gatiss have come out and said multiple times that he's dead and will stay dead. However that doesn't mean he can't still cause chaos from the afterlife

I bet they set it up to where Moran will be his successor but makes it seem like it's Moriarty

I don't watch this show, but would that be a pretty huge spoiler-y question sitting in the thread title?

He blew his fricking brains out. We saw it happen. There's no way he survived. Sherlock's "death" was obscured, so it was left open that he survived.