Same, I love AppImages for that. I just wish they also had way to contain configurations instead of putting it on the system. That would make it even more portable.

ELF and .sh files need to be set executable, chmod +x file, before they can be run, unless your DE does that for you

Dunno about appimages

also for non-KDE, non-Gnome systems, there’s appimaged – requires a little more setup, but handles the set executable, automates the AppImage integration (.desktop files and menus), keeps a watch on specific folders for new AppImages, and provides a way to check for updates

You don't install them. You just give them the permission to run and then run them.

There is no install needed, you can just edit permissions and make the file executable and then when you open it or click it the app runs.

What won't be created by default is an application menu to run it from whatever desktop environment you use. You can create those if you wish. You can create a launcher in the menu manually, or you can use a tool called AppImageLauncher to create these for you.

There's a pretty good explanation here: https://askubuntu.com/questions/1311600/add-an-appimage-application-to-the-top-menu-bar