"What questions [is/are] your data team hoping to answer?"

Solution 1:

The subject of hoping is team; questions is a red herring, as can be seen by considering How many questions...? Is or are there would not depend on whether the answer is 'One' or 'more than one'; it depends on team.

So the question comes down to "Is team singular or plural?", and unfortunately, the answer is "It depends". This question and this one address the point; my own opinion, for what it's worth, is that it depends on whether, in the writer's view, the team act as a whole (like a football team, which scores goals collectively though one person is credited) or each question is answered by one person (like a cricket team, who score runs individually, and then total them for a team score).