All you need to install your e‑Sword HD 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 tap on the "Recover Product Key" button on the popover 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 tap to be redirected to the publisher's web site for pricing/purchasing if you wish to do so.
Tap the "Resource tab" along the bottom of the app, then tap the "Installed" segment on the top toolbar. Select the item you wish to delete, then tap the "Delete" button on the top toolbar to do so.
On the first device, tap the menu button in e‑Sword, then tap the "Backup User Files" menu item. Select a shared cloud location to back them up to. Afterwards, on the second device, tap the menu button in e‑Sword, then tap the "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 HD 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 iPad models running at least iPadOS 15.0 (which is available for all generations of iPads built from October 2014, e.g. iPad Air 2.)