There is a system folder called RECYCLER on my External Hard Drive. Is it OK to delete those files? Will deleting them corrupt my file system? It takes up 15GB and I want to delete them if possible. Also, what about the files that look like _restore{0B2A276F-1DD5-45CC-A32E-C92A8BA7CBBD}? Can I delete those from the System Volume Information folder as well? That takes up another 20GB. I will be happy to be able to free up 35GB of space.

Windows creates Recycler and Sys Volume on every partition / drive.

It is created when you tell Windows to Format or Initialize any drive or partition.

Recycler is the Recycling Bin basically. You should be able to delete the files within this. The folder itself will always be recreated if removed.

System Volume is System Restore plus some necessary system files that allow recognition of that partition / drive. You can adjust the size of System Restore which by default is 12% of the drive.

To do so right click My Computer then System Restore and manually reduce the size.