Regarding your groups, and managing them... You can set up one course with groups, and manage different submission and due dates for each group.
Create groups and put the students - and the appropriate teacher - into each group.
You should be able to have one copy of an assignment, and have different submission dates for each group. To do this:
- go to the assignment
- go to Administration> Assignment administration> Group overrides
- Click on 'Add group override' button
- Choose the appropriate group from the top 'Override group' drop down
- change the dates to the correct submission and due dates
- 'Save and enter another override' until you have done all groups
When grading, your teachers will be able to select their group from the 'Separate groups' option at the top of the Grade book, and see only their own students.
Please let us know if you have problems with this, or require further clarification.