Can I paint the metal around my mirror closet slider doors?

I don’t see why not. Tape the glass, give the metal a light sanding and paint with a rustoleum color of your choice.

Yes. Purchase a metal paint any color you like. You may have to put on two coats so be sure to put painters tape on the glass. There is also a new product available for those painting windows and mirrors which is also painted on in a 2 inch width band on the inside of the frame. It dries and then protects the glass from paint. It also peels off when you are done painting. Available in the US so far.

You could either tape the mirrors or take them out of the frames and then spray paint the frames any color your heart desires.

Agree.

Yes, you can get special spray paint just for metal. Check your local hardware store.

Yes, it will be a pretty update!