It depends on whether or not he meant it in the definition of a logical fallacy or in colloquial terms. Colloquial language, if properly understood in context, is not incorrect. In one episode of The Simpsons, someone says something to Fat Tony that he doesn't immediately understand, but (to paraphrase) he replies with "In context, it is clear what you mean."

Using "begs the question" to mean "raises the question" is a perfectly cromulant application. Latin may be a dead language, but English is alive and ever-changing.

Probably, but it still sort of fits this way round and it all seems to work. Let me know if any bits fall off and I'll give it a push and see what it does.