What preview size does the Secondary Monitor use in LrC (see red arrow below)? Does it follow the same preview sizing for the main app? For example, for the main app the Loupe uses a Standard preview, Grid uses the Minimal preview.
Is this also the case for the Secondary Monitor? If I select "Loupe" in the window, does it generate a Standard preview if one does not already exist for that image?
The preview on the second monitor is the same as the preview on the main monitor. You set the preview when you import in the File Settings panel at the top right-most column of the import dialog box. If you've chosen minimal and want a better quality preview you can also choose Previews under the Library menu in the Library module.
Yes, you can choose previews on import, but that is not something that gets set in stone. Lightroom will update previews if and when needed. If you did not generate a 1:1 preview on import for example, and you zoom in to 100%, then Lightroom will generate the 1:1 preview right there and then. It will also generate new previews when you've made edits.