Restricitng the Students ability totally depends on how we are scheduling the meeting? In case you are scheduling the meeting from the Outlook Client there is an option after the Teams Meeting is scheduled.
Even after the meeting is schedule we the Teacher has the rights to make all the other members as attendee in the Teams Meeting this would help in the Two Queries you have.
For the first query can you please double check if we have assigned the Students with the Member Role in the Teams Channel. If not please change to role to Member or Student which is available in your tenant.