Depending on how you ask those questions, they may be needlessly antagonistic, so be smart about how you ask them. In my experience, most VCs will talk about these points whether asked or not, as part of their standard "this is who we are" pitch.
- Are you accredited?
- What's your background?
- When was the VC founded?
- What is the vintage year of the fund?
- How much capital is under management across how many funds?
- How much capital has been deployed out of the current fund?
- Who are your LPs?
- What is your investment thesis?
- How many investments have you made in my space?
- Can I speak with some other founders you have invested in?
Certainly, if a VC refuses to answer, or appears to try to wiggle out of, one of these reasonable questions (asked politely and in a friendly manner), that's a red flag, and you should dig further before taking investment.
Update: Thomas Ptacek points out that asking VCs about their accreditations is pointless.