What questions do they ask during the interview process at ZipRecruiter?

Beyond the soft-skill screenings from the recruiters, it really depends on what you're interviewing for, but whatever it is you're going to want to be able to tell a story about your previous experience and tie it into a pitch for how it applies to the job you want.

Depends on the role. I have a pretty unique role so my questions were tailored to my responsibilities.

This will vary by role and responsibilities, but there is a standard set of questions they abide by.