For most developer positions interviews are usually 30 minutes technical talk and 10-15 minutes question time. If I would be interviewing for a large company, I would basically ask what previous projects that they have worked, how many years they worked for that company etc.
The problem with startups are, the person that you interview with is either the co-founder or the first developer who started working there. So that person would quite likely be working there since the formation. Instead, I have asked questions about multiple office locations, languages/technologies that they use for their main product, and if they are planning to develop a new product or the if following years will be based on their current product.
I am very interested to learn about a startup's finances but was never sure if it was professional to ask about their revenue and profit. For example, even if they got $2M funding, it wouldn't last anything more than 1-2 years if their team is over 10-20 people. Since I would like to work at a place I could be financially secured, I want to know information like this. But is it unprofessional to ask about a startup's finances during an interview?