Error 1325 is a typical Microsoft installer (MSI) packaging installer permissions error (do a Google or Bing search). Nothing wrong with the package (i.e. not Esri's fault) rather it is a permissions issue with your Windows OS--and more specifically with your user account.
Can be avoided by initially running the .exe or .msi installations "Run as Administrator". But at this point suspect you need to edit your user shell in Windows registry.
1. Start with a cmd window or powershell window "Run as Administrator"
2. enter "regedit" (will have admin priviledges)
3. navigate down into your profile to:
HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\User Shell Folders
4. If the path in the data for the Favorites value, or the data fields for any of the the values, starts with other than %USERPROFILE%, change it.
5. close out of registry
6. repeat but unlike 1. run cmd or powershell with just your user privileges
7. again be sure the Favorites shell folder path points to your %USERPROFILE% value.
Those two registry edits should clear the 1325 error. But suspect you may have other partial removal/installation issues See how the ArcGIS for Desktop installation proceeds.
It is counter intuitive, but you may need to reinstall ArcGIS Pro to be able to remove it cleanly, maybe even the partial installs of ArcGIS for Desktop. A utility is helpful, personally I find the Revo Uninstaller does a good job with cleanup after an uninstall. Alternative the CCleaner -> registry mode cleanup is effective (and safe).
Good luck and post back results...
