Linux 4.15.0-88
Ubuntu 18.04
dt 3.1.0+786
Tried with folders of different sizes (about 10 to 500 images) but cannot confirm your issues 4 and 6. On item 7 : I think this is intended behaviour. See manual 3.3.11.7. In my understanding the next photo refers to the selected item in filmstrip not the image actually processed.
The picture currently processed is selected and highlighted; with a single click you can select any other picture from the filmstrip without changing the picture currently processed.
and
… You can also use Spacebar to process the next photo and use Backspace key to process the previous photo.
Are there other applications or tools running probably catching / filtering mouse events ? Did you check your mouse settings (time delay between clicks to be recognised as double click) ?