1. The idea that somehow parents are a necessary part of new student orientation is an awful development of the past few years. For generation after generation, college students have been learning how to register and macking on one another without their parents hovering nearby. You can do it, too!
I'm sure there will be a few moments when you wish your mom were there, and I'm sure there will be some other moments when you are glad she isn't and you are the envy of kids on your floor. If you have a roommate, I would be shocked if his or her parents don't try to take you under their wing a bit when they realize you don't have a parent there; you will have to decide how much to let that happen. The RAs in your dorm will help, too. Really, don't worry about this. You will be fine.
2. Minifridge: People will make it ultraconvenient to rent or buy one of these -- no need to go anywhere (but you can get better deals if you buy then somewhere far from new student orientation). If you have a roommate, try to coordinate in advance to avoid having two of them.
Oatmeal: You won't have any trouble finding oatmeal at any one of 4-5 stores that are effectively on campus, including a large Fresh Grocer and a Wawa. (You are going to love Wawa; everyone does.) You won't need any "dorm supervisor" to help. If you are willing to walk 10 minutes or so in safe areas, you can get to a Trader Joe's and a pretty good Indian market, too. And there are several periodic farmers' markets on campus, with many more a few blocks off campus (including on Drexel's campus, which doesn't feel like "off campus" because there's really no break between the two campuses).
Everything Else: I don't know the details of Penn's orientation, but I would be stunned if they didn't have shuttles to Target and Ikea. Or something like that. Also, Amazon free shipping is your friend.
Keep in mind, by the way, that you probably need many fewer things than you might imagine. It's a good idea to wait a few weeks to see what you really miss -- that won't kill you, and I think you will find that there are fewer things you actually want than you thought on move-in day.