I am trying to save my stored bookmarks and Logins, hopefully saving them when I upgrade Firefox.
When you update Firefox all your data is saved, so you don't need to worry about that.
Moving to Storage simply moves your data to your SD card.
To be clear move to SD card only moves the Firefox application files.
It is not possible for a normal user to access the Firefox for Android profile. If you have a rooted phone you can find the profile in