1) What is the runway?
When I worked in a corporate, this is not something that I ever thought I needed to know. Typically, an average corporate has a large pot of money that has been made and that gets split into smaller and smaller pots and I had to negotiate for my tiny pot as the product manager for my products. However, a startup may be revenue generating but not profitable. So it is key to understand where the company is in its profitability journey as that dictates the potential shakiness of the path ahead
2) What is the product and product strategy?
If the startup is early stage, there may not be defined product. However, there needs to be a product strategy i.e., a path to a product. If there is a product strategy, enquire and try to understand the roadmap. If there is a product, ask for a demo
3) Who is buying the product and why are they buying it (value)?
Every company needs to make money. Every transaction has a buyer and seller. In this case, why is the buyer buying? What are their motivations? and how does the product affect the buyer's bottomline? i.e., What value does this product add to the buyer.
4) What is the culture?
Talk to people who are currently in the company. Talk to people who left. Read glassdoor reviews on company culture. At the end of the day you work with people.
5) What does the org look like? Does it have the right mix of skill and will needed?
A product org includes strategists, designers, product managers and engineers. Ask yourself- Is this mix available and are the voices heard at all levels. This may be a hard one to figure out but is certainly worth asking. The question here is the current process in identifying the strategy and implementation of the same.
6) Finally ask yourself- are you ready for the risks/rewards of a startup?
Some people are more risk averse than others. It might have to do with their core personality, financial issues or other family situations. A startup could potentially get rocked by market changes and there may be organizational responses to market factors. Is this something you can handle or would this be too much? This is critical to understand and a certain level of honesty with yourself is needed to answer this question.