I've work in my fair share of startups, and even today I feel like on every new one I still miss some important questions on the interview process:
As an early member of a startup I know I'll be actually helping and leading the resolution of some of the questions, but it's important to see where the company, founders and early members stand before jumping in.
What are other questions you have asked and consider critical or important ?
I think that the issues you raise are a good start. Here are five more bullets to add to your list:
First thing: Really understand what the product/service they're building is and ask yourself "do I believe this will succeed? "
If not, leave.
If you do believe in it, then the question becomes "do they have the people/resources to enable it to succeed? "
If both answers are positive, then the only one left is "will this be fun? "
There are three important things that a startup needs to get right:
Technology, Team and Market
If you don't believe in all three, then it's not going anywhere. Ask detailed questions about all three until you are satisfied.
Another good question is "What keeps you up at night?" If they say nothing or give you a BS answer, then maybe they have not thought through their issues. If they have a litany, then maybe they just can't roll with the zigs and zags that a startup will go through.
Great answers here! More:
Nobody mentioned "pending lawsuits" question.
It's probably not the most important question to ask in general, but it happened in every startup I worked for.
Lawsuits and litigations drain huge sums of money, and have a real potential to destroy the company, especially a cash-strapped startup.
Aside from all the ones given, I actually need to know if they plan on staying in the same geographical location for long, this has been a strange recurring issue.