Can I paint a glass backsplash???

Yes you can!http://www.hometalk.com/diy/kitchen-dining/backsplashes/painted-subway-tile-backsplash-2899458?expand_all_questions=1

And for the upper cabinets, how about a deep cherry color?

Thanks! I agree for the uppers ,Have you ever used a gel stain?

Here's a Hometalker's guide to gel stain http://www.hometalk.com/diy/bedroom/dressers/gel-stain-video-tutorial-staining-without-stripping-12281731

If you're going to paint the backsplash I like the idea of the upper cabinets being a dark wood color. I'm in agreement on the deep cherry. Good luck!

I think the top cabinets would look nice in a off white (cream) wash.

I think if you put some under cabinet lighting it will make it bright, and you may find it's fine as is!

Here's a tutorial that might help - https://chascrazycreations.com/painting-glass-diy-guide-and-tips/