1. Ask if you could e-mail a couple of their clients. I used to think this was a really weird and intrusive thing to do, until I discovered the value in doing it. The clients I've talked to have been really friendly and honest about their relationships with their agents (or ex-agents). You could also reach out to clients on AW and see if they'd be willing to answer a couple of questions about their agents. I've done this before, and people here have been very open and helpful with sharing their experiences.
2. How much editing do they think your book needs and HOW LONG do they foresee spending on editing? I spent the last 1.5 years in revisions hell with my last agent, and I was definitely *not* happy with that timeline. But when I asked them about it, they said it was "normal", that this was "how things in the industry works". I wasn't okay with it, so I left, but that's 1.5 yrs spent waiting and waiting and WAITING SOME MORE. I still twitch when I think of all that time wasted, just poured down the drain because I kept accepting their excuses ("We're just so swamped! We'll get the notes to you by the end of the week!" and then come the end of the week, nothing. Rinse and repeat for months and months and months.) After leaving, I heard of another one of their ex-clients being in revisions for over a year, so I think this timescale may be normal for them. If you're okay with it, that's great, but I think this should be discussed and made clear beforehand.
3. If this information isn't readily available online, ask about their recent sales. Have they sold to houses which you would like to sell to? Be sure to Google their past sales and see how those books are doing. I made this mistake with my last agents. They were from a top agency whose name impressed a lot of people, including the agent I was interning for, so when I couldn't find much information about their individual sales, I shrugged it off and went with them anyway because hey, they're from a well-known agency, so how bad can they be, right? Wrong. When I started feeling unhappy with how slow they were being, I dug deeper, contacted more people, asked more questions...and found out my agents didn't have many sales at all. One of them only had a few sales which were mostly picture books (my MS is YA) to small presses, and the other had zero sales and she's been in that agency for awhile. I don't know how they got to be agents at that well-respected agency, but there you go. Always do your research. Being part of a top agency does not necessarily = top agent.
4. Discuss your other projects with them. If your book doesn't sell, are they interested in your other projects?
Those are really the only questions I'd ask, and if I could look at their sales on PM or their agency website myself I wouldn't bother asking #3. Similarly, if I knew their clients, either from AW or Twitter, I'd just contact their clients directly and skip #1, so I really only end up with 2 questions to ask. I used to try and gauge their enthusiasm during the initial phone call or meeting, but I dunno...I'm a bit cynical now, I guess.
My last agents were extremely enthusiastic over the phone, and then all that followed was a string of very enthusiastic excuses about how they just moved offices, how they had a bad cold, how they had to travel, how they had another bad cold, how they're just so swamped with work, how they had to travel yet again blah blah blah. I cannot reiterate this enough: Speak to their clients/ex-clients.