Can I work on my iPad only? I Mean that from one side:
I use safari and http://appinventor.mit.edu/explore/ai2/setup for building my app
And try to connect on the same device with the same device 
using app inventor companion app installed on my iPad
The result from my attempt was connection until 75% and then NOTHING
I would be very thankful to you, to helping me understand IS this possible and WHAT am I doing wrong?
I have been exclusively using my iPad since 2018 for AI2 and Kodular. It’s fiddly but manageable.
I use their respective companion apps on my Android phones via the iPad.
I use Safari. Never had any major issues.
I'm not sure.
I remember a few months ago (after the iOS release), I tapped 'Connect' then 'AI Companion' on my iPad, then I opened the AI companion on my iPad and entered the code. An error showed up and I was disconnected even before I get connected.
Because the iOS version uses legacy connection mode, it will require that you are connected to WiFi since it uses the WiFi IP address as the loopback for establishing the connection. If you're trying to do this while on the cellular network (for iPads that support it) then it won't work right now. Once WebRTC is available in the iOS version, then you should have more flexibility regarding which network(s) you use to connect.
If you continue having issues, please provide more information such as the contents of your project and which version if iOS/iPadOS you are using.