All you need to install your e‑Sword X module at no additional cost is to enter your Email address and "Product Key" you received when you purchased the module for use with e‑Sword. If you do not have that information, just click on the "Recover Product Key" button on the dialog that prompts for this information.
When you attempt to download a "locked" module it will display a dialog prompting for your "Product Key". On that dialog is a "Purchase From ..." button that you can click to be redirected to the publisher's web site for pricing/purchasing if you wish to do so.
On the first device, select "File, User Files, Backup User Files" menu item. Select a shared cloud location to back them up to. Afterwards, on the second device, select "File, User Files, Import" menu item. Select your user files from that same shared cloud location. These steps are also how you backup your user files for safe-keeping.
No. E-Sword X is an "offline" app. An Internet connection is only needed for downloading the app itself, and any additional modules you wish to install.
No. Only Mac models running at least macOS 11 Big Sur which is available for all generations of Mac built from 2014.
Check out the online Help file here:
https://www.e-sword.net/mac/help.htm
Kevin Purcell has created a great online demo you can view here:
https://www.youtube.com/watch?v=R3kL_uGrWcI&feature=youtu.be