It replaces templater code within the currently open file, so you don’t have to load an external template. Like, you type <% tp.file.last_modified_date() %>, then press Alt/Opt+R and you’ll get the file’s last modified date and time.
I never had much use for this (except for testing), since the templater code is replaced with its result and thus gone afterwards.
Nope. If you find one, let me know 
Then again, Obsidian’s File Explorer pane shows the last modified date if you hover the mouse over a file, and it could possibly be retrieved “live” using the Dataview plugin.
We must remember, after all, that Obsidian is a system to create/handle plain Markdown text notes and not a “live”, variable- or event-driven system like a website could be.