Yes, this rangefinder will work on a compound bow.
The screen is a black background with green and yellow text. Here's a link to the manufacturer's demonstration video where the screen is shown.
https://youtu.be/AGfjaN6hQF8?t=305
Yes, this is capable of being mounted to crossbows and should be compatible with that crossbow.
Yes, the optic will include 1x CR2 battery.
The laser range finder is powered by 2 CR2 batteries.
No, it should not get in the way of cocking the crossbow.
It will most likely not fit. The crossbow mount is a ring adapter that mounts to the scope on your crossbow. If the crossbow scope doesn't have at least 1 inch of mounting space on the main tube this cannot be mounted to it. You may be able to mount to another point on the crossbow, but it is meant to be mounted to a scope main tube.
The range finder will come with both a crossbow and bow mount. The crossbow mount is a ring mount meant to attach to the scope.
This comes with a mount that attaches to the 1" tube of your crossbow scope.
Yes, you should be able to mount both, as this mounts on the other side of the bow from the quiver.