I like the “class room” name @Tuomo 
For each “class room” we could create a private forum section just for the students who enrolled on that “class room” session. That way it won’t annoy students who aren’t interested and also it gives a non-public place to share performances and ask questions.
We mentioned a 1:1 aspect to each “class room” program. These 1:1 sessions could be recorded and then posted in the private class room forum thread so that the participants get the benefit of their own 1 on 1 session and also the other recordings as it’s the same topic that everyone is studying. That seems like a good way to maximise the benefit for everyone.
We have a forum section called “Testing” which is just visible to me and the developer of the website. This allows us to test things without annoying everyone else 
It would be the same idea, but we would call it “Feb 2021 Class Room” or something to do with the topic/theme. This would be the place where the assignments, quizzes and study materials (courses, lessons, seminars, audio exercises etc…) are posted. This would also be the place for asking the teacher questions and posting videos/audio/performances for feedback.
All of the above is simple to implement from a tech/website standpoint.
The following 2 aspects of the initiative would need some consideration:
1) Software for quizzes
We already use a service called TypeForm for student feedback and new student orientation. This is really great software that can be embedded into both the forum and the website. Here are some example of TypeForm quizzes:
Tuomo and I will create an example quizz this week and post it in this thread.
What i like about TypeForm quizzes is that they have “conditional logic”, so based on the answers the student gives, the quizz can recommend the next steps, ie. specific lessons to watch to improve on the areas that were answered incorrectly.
2) Software for the 1 to 1 sessions
Tuomo and myself have the equipment to set up an overhead camera shot of our piano for these 1 on 1 sessions.
I’m unsure what software we would use for to connect the student and the teacher, and record it. Perhaps Zoom or something along those lines.
It would be great for the discussion and questions between the student/teacher to be captured in the recording and that way when it’s posted in the private thread, all students on that class room program can benefit.
I will do some research this week for some suitable software 
Any comments or ideas welcome!