No. The main requirement for a DMCA request to be valid is that it come from a real entity. If you sent them with a fake return address they wouldn't be valid DMCA requests anymore.

That said, yes the DMCA can be abused. The check against that is the same check that exists against other kinds of fraud: it's illegal.

Yes. But in that case, GitHub would likely fight an obviously fraudulent copyright claim, as it would wreck their business.

They're not hurt at all by popcorntime going down.

I don’t know, they seem to be being hurt a bit in the eyes of developers right here in this discussion.