How do you completely turn off update checks in Firefox v64?
You can use a policies.json file to disable updates for all users.
https://github.com/mozilla/policy-templates/blob/master/README.md
or
https://winaero.com/blog/disable-updates-firefox-63-above/

Note that the OP wants to use Firefox 52 ESR, so the policies.json solution doesn't apply and using app.update.enabled = false should be sufficient.

(edited; portable version not available for Mac)

Installing multiple versions on Mac OS X is basically dragging the Firefox application out of the DMG file to the desktop and rename the folder. You can drag the renamed Firefox application folder to the Applications folder like you would normally install Firefox. You can possibly eject the DMG file and and trash the installer.

You need to use the terminal to create a new profile for that version. Firefox also comes with the about:profiles page that has a button to create a new profile. Make sure that no profile is selected as Default=1 to make the Profile Manager show when you start Firefox. You can check that in the profiles.ini file.