Thanks!
The game does capture the mouse but I also noticed that it doesn't seem to work properly on a windowed web version. Maybe another weird Unity 6.2 bug, I encountered several...
I already improved piece visibility multiple times by adding those outlines, making them more distinct and thicker several times. It's rather hard to have nice glowing outlines with distinct colors for 9 pieces (the emissive sun and white dwarf don't have one). I tried a lot of different colors.