I would say inquiring about funding and research opportunities is definitely important if you haven't yet done so and if it hasn't been adequately explained on the department's website. I only found out the full extent of research funding during my school visit for one of the programs...it wasn't described in detail on the site or in the grad bulletin, so I'm so glad I asked about it!
Other things I might ask about: how advising works/how often you might be meeting with your advisor...how independent studies credits work...what kind of graduate facilities there are (i.e., cubicles of private library space, kitchen or fridge for students, lockers, keys to the building, etc!)...