ren "C:\Users\username\AppData\Local\Windows Live" "Windows Live Old"
For example, yes. It's probably easier just to right-click on the folder in Explorer and select Rename.
... without Windows Live running then try WLMail and see what happens?
No! The program will undoubtedly run as usual whether that directory is there or not. The only situations where you would need the cached installers are when you need to repair or uninstall. wlarp.exe is the applet that launches a repair or uninstall operation (Windows Live Add/Remove Programs). If you can successfully run a Repair ... after renaming the Windows Live folder, you clearly don't need the files in that folder.