Probably most will refuse. That's when Congress has to sue. This also happened in Watergate. The committee subpoenaed the tapes, and Nixon refused to hand them over (claiming executive privilege). Eventually, the Supreme Court forced the administration to comply. One major difference here is that the Court is occupied by GOP sycophants who have no trouble violating their own stated principles in service of the GOP's agenda. Like with Watergate, getting at the truth will depend entirely on enough Republicans turning on him. If the Grassley/Graham questioning of Fusion GPS is any indication, we have a long way to go.
As to your second question, my gut is to not dignify it with an answer. However, it should be pointed out that it is explicitly stated in the Constitution that a member of Congress cannot be arrested when traveling to/from Congress or when in session.