Educational Groups, User Types & Access Permissions

I'm about to install an Elgg SN on an educational support website I manage. Does anyone know if it's possible to have both public and private groups in the same SN. Essentially, I need to have open access for teachers and restriced access for students.

#1 Could a teacher create a group for his / her students and set it up so that only those students can access the group, discussions, etc.?

#2 Could a teacher then choose to share access with another teacher's group to allow a collaborative exchange?

Any advice would be much appreciated.

Kind regards, Richard