How to install PSE catalog on drive C and media on drive D

. . .  and in future, make sure you backup the catalog (and your photos) on a different drive.  You can simply copy the catalog folder using Windows Explorer.  Hopefully, you won't have another C drive failure.  But if you do, you will not lose all your tagging and face recognition etc.

BTW, when you do the bulk import, any keyword tags that you had previously given to your files can be imported into the new catalog.  However, any system tags (People, Places, Events) will end up in the Imported Tags category.  It is fairly easy to recreate the People tag hierarchy, but you will not have any face recognition for those People tags.  You may just want to allow face recognition to proceed again.

Yes.  The catalog's folder structure panel will follow the D drive structure.  (But make sure you are in Tree View not List View in the My Folders panel.)

The catalog and your media are entirely separate.  We need to know a little more about your situation to offer you some advice.  You are the one who selects where your media is stored, not the Organizer.  The catalog is just a database of your media files wherever they exist.  However, once you start using the Organizer catalog, all of your media management (move, rename, delete) should only take place within the Organizer.

If you have not yet imported media to your catalog, you should move or copy the photo/video files to your D drive and import the files into your catalog from there.  If the media files are already in your catalog, you can (and should only) move the files using the Folders panel in the Organizer.

You can manually move the catalog folder from its default location on the C drive to your D drive using Windows Explorer.  (You can find your current folder location by going to the Help>System Info dialog.)  Move the folder and all of its contents.  Then find the catalog.pse24db file within the folder and double-click on it.  The catalog will open in the Organizer.

If I have not covered your situation, please give us more details about the status of your catalog and media files and exactly what it is you want to do.