Part Time Minus is probably just the hospital's term for part time staff. It also might be a position that does not include benefits (minus benefits). You could call the HR at that hospital and ask. I'm sure they would know the answer.
PRN and per diem both mean the same thing- "as needed." It means that you have a minimum number of shifts you have to work each month (maybe 1-2 per week). You will sign up for shifts after the regular staff (if they do self-scheduling), or you will be scheduled in the open slots. If there are too many staff assigned to work, you will be the first cancelled. Again, you'll need to call HR to find out what each hospital's specific requirements are. These positions are usually paid more per hour, but you don't receive benefits or accrue paid time off. You also aren't guaranteed any hours.