iWork apps are notoriously not backward compatible. I am doubtful that a document created in 13.1 will open in version 11. And one created in 11, then opened & saved in 13.1 on your other Mac, will no longer be readable in 11. Maybe someone here knows for sure but I wouldn't bank on any of this working.
If you need compatibility on an older machine, you may have to use iCloud Numbers. It is always the most recent version and, being web-based, can be used on older Macs. This also means storing your documents in iCloud so they can be accessed.
But you should be able to update your older Mac well past 3.6.2. Usually all you do is go to the App store and an Update will be listed. Before deleting 3.6.2, make sure Numbers is in your Purchased list (click on your user name to see the list). If it is not there, you will not be able to download any version of it. You can download the highest compatible version from your Purchased list, but not from the main store. The main store has only the latest version and it will not let you download that one unless it is compatible with your OS version.