Please see answers inline~
Where does Shavlik Patch download the patches to before they are published into WSUS?
The patch are initially downloaded to C:\Users\adminname\Shavlik\ShavlikPatch, the CAB file is created here and verified to be valid. The patch is then moved to C:\WSUS\UpdateServicesPackages for more verification and then finally moved to the WsusContent folder. The default location is C:\WSUS\WsusContent, this location is controlled by WSUS. You can verify the location by opening a CMD prompt and typing 'net share', this will give you the share location for the WsusContent location.
Does the patch download happen during catalogue synchronisation or when they are published to WSUS?
The download happens immediately during publication of the patch.
Do the patch files get transferred into the WSUS updates location when they are published?
Yes, once the patch is download to the WsusContent location SCCM/WSUS will distribute it out to the WSUS server and then to other sites if configured to do so.
What the options for rollback of a patch with Shavlik Patch? Is it custom actions and scripts?
There is no rollback function.
Please let me know if you need anything else.