1. I'm not sure about this one. If the LUMIN U2 Mini is still on (you haven't flipped the power switch on the back) then leaving or closing the LUMIN app should not affect the unit. It will still be on, and stay on, playing music you already queued up, etc. None of the LUMIN units turn off when you close or force quit the LUMIN app. It might have gone to sleep eventually (check your device settings in the LUMIN app) but it should still show up and you should still be able to use it when you reopen the LUMIN app.
2. I think you meant to refer to the Qobuz Playlists grid/list item in the main panel to the right side of the screen? When you have Qobuz selected from the tabs? Those are Qobuz playlists and not the LUMIN queue or a LUMIN playlist. If you want Qobuz content to show up in a Qobuz playlist, you have to explicitly add content to an existing or new Qobuz playlist. Press and hold on something and then select "Add to Qobuz Playlist". This will only add it to a Qobuz playlist–it will not also add it to the LUMIN queue.
3. The things listed in the left side vertical list is your LUMIN queue. There are no meta-reorganization functions to manage the queue. Things are added the way you chose to add them. You would have to manually redo it.
4. I have not heard of this happening before. You should probably reach out to LUMIN support. Maybe it is related to the issue you are describing in #1.