Indeed frames have styles but they cannot be directly accessed from some specific menu item.
Open the styles panel with F11 or Format → Styles and Formatting. The frame styles are listed when you click on the third icon from the left in the toolbar.
As you can see, there are very few built-in styles. Feel free to define those you need.
Template: from the start, it is only a document like any other. It becomes a template only after you save it as an .ott file. Juste double-click on its icon and it opens a new untitled standard document.
Caveat! Whenever you modify your template, it is once again considered a normal document by LO and you must “save it as …” an .ott file so that the changes are incorporated into the template.
Register: the term is ambiguous. A document becomes a template when it is saved as .ott. “Register” may also mean “integrate” the template into the LO implicitly known template set, so that File → New → From templates (exact wording from last item varies with LO version) shows your preferred templates (usually from My Templates). Templates can be managed by LO without the need for fiddling with complex procedures.
However, the templates directory is usually deeply burried in a hidden configuration directory which is not convenient when you move things around. You can change or augment the default location through Tools → Options..., item Libre Office → Paths. Click on the Templates line and Edit....
For instance, the desktop.org specification now defines a Templates folder in the user directory for that purpose.
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