Do the HSRP group IDs configured on Supervisor Engine 2/MSFC2 have to be contiguous? Are there any other requirements?

The HSRP group IDs do not have to be contiguous. You can pick any 16 group IDs in the allowed group ID range (0-255). However, only 16 group IDs can be used from that range. MSFC1, MSFC3 (Supervisor Engine 720), or MSFC2A (Supervisor Engine 32) can use any number of group IDs from that range.