While I didn't go to USF, I did consider it briefly for undergrad (I got in but didn't attend). I don't know anything about the program to which you refer, but I can answer your questions about the religious affiliation and academic quality. To clarify, USF is a Jesuit institution.. while it is Catholic, the Jesuits are (in my opinion) the most liberal of them. There are requirements for religious classes for the undergrad core, but I don't think there is for grad school. People on the campus don't go to USF because it is Jesuit. There are a lot of local people on the campus, so as a result there is a vast mix of religions and cultures among the student body.
I had a good friend who used to be on faculty in the School of Nursing (undergrad and grad both), so again I can't speak about the academic quality for your program.. but from what I understand, the academic quality of the student body in general has definitely declined in recent years. To clarify: the professors are top notch, but the students are not. I'm sure you would have no issues getting an internship and relevant work experience (side note though- public transportation to the south bay from SF isn't very good, you would need a car) as a USF student. My personal opinion on USF would be if you have to pay out of pocket for it, I would think carefully about it before committing.