OK, I have found the answer. XposedMTCManager was guilty - disabling it resolved all issues with no logo at boot and black screen.
@Malaysk Below is the issue and solution - could be pinned on first page. If someone can add / edit that better - feel free to do so:
Issue: black screen at recovery / no Android logo and no first part of the logo loop during boot / black screen after boot but HU working in the background (touchscreen works even though it is black) / black screen immediately after pressing one of the physical buttons (depends on model)
Solution:
1. go to Xposed Framework --> Modules
2. find module named XposedMTCManager
3. Untick the checkbox next to it (in other words - that module should be disabled)
4. Restart HU
5. Initial logo at boot should be visible now and no more issues with black screens
PS I have noticed that after installing Fuse ROM from scratch with full wipe - that module is installed but not enabled by default. Enabling it causes the issues described above. Was this meant to do anything elese... or am I missing something?
I hope that some of the users may find this post useful