Why do some applications not appear in the menu after installation?

That is the probably related to your flatpak question.
If an application doesn't use a generic manner of adding a menu entry but i.e something very specific for a targeted distro (like Ubuntu), then it wont show up in the Elive menu.
If you've got cairo-dock running then that'll have a menu that can differ from the left-click menu on your desktop.

Of course you can always try a search with for your application.

Considering your configuration issues, I also would recommend going through this post: