Could you open Disk Management and post a screenshot? It would help to see exactly how your hard drive is partitioned. Please maximize the Disk Management screen before posting. How To Access Disk Management in Windows 7 Screenshots and Files - Upload and Post in Seven Forums
The System Reserved partition contains Windows 7 boot files. If that partition is damaged or deleted it's likely your computer won't start up. Yes, it is possible to split the C: partition into two separate partitions. You would shrink the C: partition and make it a smaller size. This would create empty disk space called unallocated space. You would use that unallocated space to create the new partition. Partition or Volume - Shrink Partition or Volume - Create New
Yes, you could use that new partition to store backups. But I don't recommend it. If the hard drive ever fails, you could lose everything on it including backups. It would be much safer to store your backups on an external hard drive.