You can paint the brick, but then you take something that is basically no maintenance and turn it into something that has to be repainted periodically. You can also stain brick.

Brick needs to breath. You have to get a paint designed for use on brick. If you use any old outdoor paint moisture builds up in the brick and it will deteriorate. I suggest stain if you must change the color. PS Brick is not meant to be painted. That is the wonderful thing about brick it is virtually maintenance free.

Sure but be ready to repainted later, paint will peel off after a while, personally I would clean the bricks power wash them but no paint, why create a job when you don't need to !