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1. OK is useful. but is not in manual on electrum.org
2. 3. 4. I see file Electrum-4.5.8.tar.gz in my computer. Yes is unpacking, and work. mean must be downloaded.
For the AppImage having no instructions, that's because its not specific to Electrum but applicable to any AppImage binaries.
And since directly running the extracted tar.gz works, you can use it for now until the issue with your OS is sorted out.
You can easily restore the wallet from seed in case you'll have to create a virtual environment to properly install it as instructed in the link below.
For a possible solution, read this thread from Linux Mint forum:
forums.linuxmint.com/viewtopic.php?p=2505685But I'd recommend to just launch it without installing if installation doesn't work without a workaround solution.