That’s already been adjudicated in prior Court cases. He wouldn’t have to explain anything.
Besides that, though, that wouldn’t stop Biden from being elected President. He could simply appoint another VP to be confirmed by the Senate if somehow she were found to be ineligible.
Not in terms of Presidential eligibility at SCOTUS. SCOTUS has acknowledged the definition known to the framers and founders in other (non Presidential) cases....and she is not eligible. However, they haven't decided a case specifically on the question of POTUS (or VP) eligibility.
Additionally, the states electors vote once for President and once for Vice President. [1]
The courts would be inundated with lawsuits if a majority of states EC votes went to a not eligible vice president.