Ask (the) Interviewer?
When I introspect the recent hiring event for my team one thing that differentiated some discussions from others was the participant's curiosity to "know more".
While many participants chose to ask standard questions about the role I cannot forget some discussions because of some thoughtful and challenging questions from the participants.
What would my work look like for next quarter :
I would rephrase the question as tell me my 30:60:90 day plan. A very important aspect not only for the participant but for the hiring manager is to plan and articulate crisply to the candidate. Some organizations are even publishing 30:60:90 plans in their JDs as well.
Top(2/3) challenges for the team and how will my skill set helps:
Every team has myriads of things "to do", and the answer to this question lays the foundation for the most important items you should focus on when you join the team. This may mean acquiring new skills, researching ways to solve the problem differently, and thus differentiating yourself quickly.
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What are the growth opportunities within the team & organization:
You are not switching for the short term, it is an important decision and the answer to this question will help you understand the company's culture on how talent is recognized and rewarded. It could be growth(promotions) or lateral movements, ask for some specific example(of course no names).
Is this position a replacement backfill or for a new project:
For backfill positions, you can expect most of the process will be in place and you may have a smooth ride once onboarded. In case this is for a new project check the current project state, skill set required for the project, how many team members are already on board, would it mean some extra work late evenings/weekends, etc.
Overall I enjoyed these questions and any Interviewer would expect these questions from a candidate who is seriously considering the position. Asking these questions will help the participant set his expectations right and limit the "surprise" when on-boraded.