Keith
What computer operating system are you running Premiere Elements 12 on? For now I will assume Windows 7, 8, or 8.1 64 bit.
You cannot move, delete, or rename folders files that go into a project after you save close the project. If you do so, you are heading for nasty media reconnect issues which you will probably need to correct with the "Where is the file.....?" messages.
Bottom lines for you to explore...
Start a New Project..
Edit Menu/Preference/Scratch Disks. Point them to your external hard drive, make sure there is enough hard drive space at that location.
And, then move forward with your project unless you have the time for probably a lot of reconnects in the project involved in your organizational attempts.
The project file is saved as per the Save In in the new project dialog. File Menu/New/Project. Set that according otherwise the project file will probably head to 12.0 Folder in the Documents.
The rest of the story....
You wrote
Do I need to save the (Adobe Premiere Elements Auto-Save, Adobe Premiere Elements Preview Files, Adobe Premiere Elements Preview Files, Adobe Premiere Elements Preview Files, and the LRV’s and the THM’s)?
I am not sure what that is all about when you triplicate the Adobe Premiere Elements Preview Files Folder. And, what are the LRV's and THM's? Be that as it may...
The folders that you are finding in Libraries/Documents/Adobe/Premiere Elements/12.0 will regenerate automatically for each project even if you delete them..You can minimize what is in them----
a. You can disable the Auto-Save feature in Edit Menu/Preferences/AutoSave, giving you an empty Adobe Premiere Elements AutoSave folder.
b. You can delete the preview files (rendered files) in the Adobe Premiere Elements Preview Files Folder, but then, when you are in the project, you will get an orange line over your Timeline content pointing you to Timeline render if you want the best possible preview of playback of the Timeline content in the Edit area monitor. .... the program's search for rendered files seems to be related to your reorganization scheme.
c. You can delete the content of the Media Cache Files Folder (conformed audio), but the program will automatically regenerate them if and when it decides it needs to do tat.
I would encourage you to set up a maintenance program to avoid pile ups of preview files, conformed audio, and conformed video, but they are a fact of Premiere Elements life. And, you should be aware of the consequences.
Lots and lots more details.
Please review and consider and then we can decide what next.
Thanks.
ATR