1. Explain the difference between a hot backup and a cold backup and the benefits associated with each.
A hot backup is basically taking a backup of the database while it is still up and running and it must be in archive log mode. A cold backup is taking a backup of the database while it is shut down and does not require being in archive log mode. The benefit of taking a hot backup is that the database is still available for use while the backup is occurring and you can recover the database to any point in time. The benefit of taking a cold backup is that it is typically easier to administer the backup and recovery process. In addition, since you are taking cold backups the database does not require being in archive log mode and thus there will be a slight performance gain as the database is not cutting archive logs to disk.

2. You have RMAN database backup excluding controlfiles. how you will proceed for recovery?
We can manually create controlfile with new location for datafiles and redolog files (or if we already know the location, we can use that) and once controlfile is created, we can mount the database, restore the database and switch datafiles. Finally use resetlogs to open the database.