These suggestions are just MHO, of couse, and I'm sure others will be along shortly with more ideas.
Re: eating, yes, it is very easy to snack all night when you're working 3rd shift. What I do is eat the three regular meals/day that I would eat anyway; I just spread them out differently -- I eat breakfast when I come home, before going to bed; I eat a regular meal in the middle of the evening, before going to work, and I eat one regular meal (little or no addtiional snacking!) during the night at work (same as I would on days or evenings), usually right around the "halfway point" of the shift. Lots of hospital cafeterias aren't open on 3rd shift, so you may need to bring your dinner if you don't want to have to improvise from snack machines (v. bad idea!) Of course, there's often the possibility of ordering out, too, but that can get v. expensive.
As for sleeping, that depends on how often you're going to be working night shift. If it's just one or two nights a week for many weeks, I would stay on a regular, diurnal sleep schedule; work the night shift, go home and sleep for a few hours (4 - 5 max), then make yourself get up and go to bed at around your usual time that night. If you're working most nights for a shorter period of time, then it would make sense to grit your teeth and "switch over" to sleeping days/staying awake nights (as much as your school schedule permits) until you're done with the nights rotation. It's the switching back and forth from one schedule to another repeatedly that really gets you!
I really hope that you aren't going to have to work all night and then stay up to attend class the following mornings -- that can be done, but it's really brutal (again, IMHO). Good luck, and congraulations on being so close to graduating!