Serious question: Could Cruz be elected VP without legal questions being raised?
The same qualifications apply to both offices. The questions of whether and how the issue is raised and handled are independent of whether he is qualified. He's naturalized, the precedents are clear and settled.
Legal qustions were raised about Barack Hussein Obama, II.
226 lawsuits were filed challenging his eligibility as a Natural Born Citizen. That didn’t stop him from being elected and reelected.
Moot question. At this point the only person who can beat Cruz for the nomination would be Trump. And Trump can't be expected to select someone he doesn't think is qualified for the office.
No. The qualifications for VP are identical—since his principal function is to succeed to the Presidency if necessary.