Oh sorry, I hadn't read your Q very well.
Some questions would be:
- Considering that I was not accepted to the program, were there any specific reasons why I was not accepted? Related to this question, what could I do to make myself more competitive? You can ask about any gaps/weaknesses the POI has seen in your CV, references, interview, etc.
- What are the strengths in my application and interview?
- If you'd like, are there any opportunities to work with you as a research assistant/to publish something, etc.? This is to maintain the relationship and gain some good experience if you want to