1. Apps can check if another specific app is installed without the need for any permissions. That is how Privacy Browser checks to see if Orbot is installed and displays the version number in the About screen if it is. However, the ability to do so might be limited to asking by name if a specific app is installed, and thus doesn't allow the enumeration of all apps.
2. Apps can register an intent with the OS that lists what types of things they are able to open. Privacy Browser uses this list for the share functionality. This doesn't currently work with YouTube or NewPipe, probably because Privacy Browser shares both the website title and the URL in a way that works well with sharing to a message or email.
3. I should be able to create a different menu that shares just the URL in a way that other apps can open it up (URI format will probably work best). I will look at adding such a menu when I get to this feature request.
4. Some apps might need to have a specific intent to work correctly. In addition to the above list, I should probably also look at opening F-Droid as well.