I'm in similar situation. Met my current tech co-founder 3 weeks ago and I'm joining them as a co-founder.
See that you believe in the project and are looking for signs to tell whether it's a good fit. Here's my experience: Ask yourself if you can trust them. By trust I mean two things.
One, professionally, can you trust their judgement?
Can you work comfortably knowing that they're going to make decisions that will literally determine the growth/death of the company? You don't have to face this when you work in established companies because no one will have that impact. But in startups, a few wrong decision can turn things bad. If you don't have domain knowledge in what they're working on, you need to be sure that the team is capable in identifying the market and executing the biz.
Two, personally, can you be friended with them?
Are you comfortable to spend days and nights with them? I've only started working with the team 3 weeks ago and I'm now working with them every weekends. On weekdays, I generally work till after 9:30pm. Are they smart to spot the key, proactive to fix stuff, open to challenge, honest in telling the truth? These are all very important elements that you have to look for if you're to spend lots of time with them.
You can't get the real answer until you start working with them. Here's what I did: I worked with the team for free, without any talk of equities. Everyday I just find things that I can contribute and no one in the team can do the same. The founder is very open to me. That helps us working out together. I'd say we just "fall in partnership" without much "discussion". We observe each other in rounds of negotiations, customer meetings and internal discussions. I keep looking for evidences that the project and the people are "for long term".
Of course, it does't mean you have to do the same. But I'm suggesting that you look for opportunities to get into real work with them before jumping in, even it's a mini-project. It helps a lot in collecting crucial information. Regarding questions to ask, probably it's about their business just to start with. If even the founder couldn't explain how it works, what problem it solves and where's the market, that's the red flag.
Feel free to write to me. My blog & contact in profile. Recently I wrote 3 blog posts on deciding between startups and corporate jobs and you might like to see.
Hope it helps. :)