"I'm not sure if I can delete these files"

It seems someone put the Working file (.qbw) on the desktop; you are seeing the associated Utility files.

Make a backup as usual. Now use it to Restore to a proper folder such as My Documents or Public Documents, Intuit, QB, Company Files:

Restore a backup company file

Don't forget external files:

Restore custom templates and forms

Once you get this all working with the file from the new location, it will be safe to delete the Desktop working file and its associated utility files and subfolders.