Can I assign to more than one class/group at a time?

No, for ease of recording your assigned zApps and zApp Books, you can only assign to one class/group at a time.

If you want to regularly assign the same work to two classes at the same time and with the same conditions, you could create a large class that combined class A and class B, thus enabling you to send to both classes simultaneously. You might then Create 2 subgroups, one containing the students in class A and the other containing the students in class B for the occasions when you want to assign different work to each class. There will be some disadvantages to this in terms of ease of assigning an iQ to just one class for example or managing reports.