A better approach is to dive into the product and make a judgement... "What does the company need to do to secure its next round of funding?" VC-scale rule-of-thumb is you need a new funding round every 18 months... 12 months to improve the metrics, then 6 to close the next round. Figure out when the last one was, when the next one comes due, and how honest the company goals are from now until then.
If I join the organization without asking these sorts of questions and realize that the person leading the company doesn't even know how their own company is running that kills my morale. It could also be that when I ask these sorts of questions I am frank about my opinions: I don't mind being part of the machine but I am business oriented and derive motivation/happiness from doing what I can to accelerate that business even further.
Even if they don't offer equity, you still have a significant opportunity cost and risk when you decide to work for a startup. These questions attempt to quantify these.
And rightfully so.
Employee is investing time in effort and receives compensation and equity in case of startups. If equity is non-zero, then obviously employee will ask the same questions an investor would.
Salaries in startups are lower than in most corporations - the difference is what employee might consider to be their cost of investing in the company.
Yes, this is a warning sign. A CEO of a startup should know that employees take on risk by joining and that prudent candidates will want to take the financial health of the company into consideration when comparing offers.
Runway length - Similar to above, trying to gauge if the company is self propelled or not
If received funding, how much and when was it received, also ask for burn rate here.
Very quick estimate of company health = Revenue per month - (burn rate per month + (head count * average monthly salary)).