How from the Template Manager do I determine the path where the templates are kept?
The path to templates is defined from the menu Tools > Options. Please see the following Q&A.
From the Template Manager you do have the option to move one template to another folder. For LibreOffice 4.0 and newer, you can do this with the button labeled “Move to Folder” (“Mover a carpeta” in Spanish in the image below).
Click on the image to open a full-resolution version.
Image from this answer on Super User by myself