Hi

Mop up round is done to fill vacant seats in 15 percent all India quota.

These seats are in hand of respective states and states can look after those vacant seats.

Once, second round of counseling is done, list of vacant seats are released by NTA and then registration starts for Mop up round

Deemed universities can give these seats under management quota.

Yes, you have to apply for Mop up round on mcc.nic.in

Best of luck