It may not show up in your library based on what they are saying. This is a publisher distribution licensing issue. But, you should still be able to log in to Amazon.com (ie US) and read it in the web reader, or on a different device.
The documented way is to use the Kindle PC app and download the book inside that. The file will end up on your PC and only readable in the Kindle. The current versions download the book as a .kfx file that allows Kindle apps to do more with the data. Older versions downloaded the file as a .azw file.
The USB option does need Kindle hardware. The hardware ...
You can't, that's part of the Amazon security, they don't want you making copies. And it's illegal to make unauthorized copies of a book with copyrights.
If you want to search around on the Kindle itself, connect your Kindle to a PC and it should appear as a drive. Look for a bunch of MOBI or AZW files. Those are your books. Except each book does not have ...
Usually, the ISBN number is supposed to change when the edition is modified.
The modifications may be minor and not matter much to readers.
The publisher is not supposed to change the text, except for typos and such,
though that could depend on contractual agreement in some countries. It may
also happen that some parts of the text have different versions, ...