My answers:

-- He would not be legally culpable, IMO, but some people might view him as morally responsible/partially responsible. Definitely not a "terrorist" in any way, shape or form.

-- To add a fact to your hypothetical, let's say that Omar repeatedly and clearly called for violence. Then, I think he might be guilty of a crime, although you'd have to ask a lawyer what the specific crime is. I still don't think it would be "terrorism", though. It's just something like incitement to riot or whatever the correct legal terminology is.

Last point: Be careful what you label as a lie or, better said, what you think should be punished as a lie. There's a huge grey area here, and I think we should err on the side of free speech even if it's repugnant or potentially dangerous speech.