Oh, I hate the name issue. It never ends! I'm from a small liberal arts college in the Midwest too, so I'm accustomed to calling a lot of my professors by their first names as well. As far as I can tell, it's okay to use a first name when they either introduce themselves that way (just their first name, no last name) or sign an email with just their first name. Initials as a signature or first name + last name still mean that you should call them doctor or professor.
It's possible that the grad students weren't using her first name because they assumed that she didn't want you to use it. That happened at my last interview. I was never given any indication that I should use first names for professors at that school, so I don't. The students would call them by their first names unless they were speaking directly to us prospective students, in which case they would refer to professors using their titles and last names.
A professor at a different school signed her emails to me with her last name until she invited me for an interview, when she immediately switched to first name. When she switched, I did too. Her grad students use her first name and her undergrads use her title and last name, so I think it was a nice gesture to switch to first name with me. My point is, it meant something. Definitely be careful with the name thing, in all contexts! I think that students like you and I have to be particularly aware of it because we come from schools where first name is the norm.