Shadowing analysts

I think one of the most important things to gauge would be the level of busyness for the analysts you shadow. You are there to learn as much as possible, but they are their to work their asses off. If it is clearly a slow day, ask a lot about what they're doing and how they handle the deal process. Some questions I would initially ask if things are relatively/somewhat slow are:

1. What current deals are you working on
2. What role do you provide on each (e.g. due diligence, modeling, CIM building, and how he or she does each part)
3. Ask about their backgrounds; how did they end up at XYZ firm, what helped them excel at a junior level, what are their interests external to work

I think you're in a fairly unique situation, so just making sure you are mindful of the analysts' time is paramount. If they are swamped, maybe you are just watching quietly and listening to their interactions with the other deal team members and sitting in on calls and meetings.