I believe in home births. I might have a hospital birth if I can have a midwife and no students. Is that possible?

Yes! You may need to ask around but many places have midwives. And you should never have to have a student. That is always your choice. Don't discount doctors though. Some doctors are really open to having a low intervention births that are more home like. Good luck!
You can where I work. Local options vary from community to community. In one of two local delivering hospitals, the local ob's have several certified nurse midwives who deliver in the same ldrp suites used by the physicians & have the benefit of almost instantaneous backup & assistance if a problem arises that requires advanced care. The choice of who attends the delivery is that of the mom involved.
Yes. Ask your midwife. She should know those answers or be able to get them. She will have hospital privileges and any one can request no students to be in the room.