If you're going to be paid in equity and not asking those questions, unless it's a publicly traded company (where you have these answers ahead of time) or you are getting compensated well above average in cash equivalents, it would be just plain irresponsible to not ask those questions.

Even if you are getting paid an extremely good salary, who wants to start working for a company that's potentially months or a year from becoming insolvent? The fact that this might not be standard due diligence as suggested by your comment is mind boggling to me.