Does this place allow you to choose when you want to work each week? Like if I only wanted to work 2 days can I do that?

No. You have a set schedule. So if you can't make your days I'd suggest you look elsewhere or pick a different shift.

You have a weekly schedule. You also have PTO(paid time off, Vacation and UPT(unpaid time off). If you only want to work two out of the four days you're scheduled for, you'd have to cover it with your PTO or Vacation time in order to get paid. If you don't, your two days will automatically be covered by your UPT. I'd try to use as less of UPT as possible, by the way.

Not that I'm aware of.