The brick can be cleaned but if you must ask how,I advise hiring a pro. Reason being that a wire brush on a drill will remove drips but might also damage brick so one has to know when to stop and try something different before doing too much damage. Acid wash will remove most white discoloration but is dangerous to use. Some might suggest pressure washing but can blow mortor out if it is soft.

I would hire a professional to clean the brick, and hopefully, it will look good when done. You cant paint over it unless its clean anyway.

The white stains look like efflorescence. Try a stiff brush and a gentle dish soap, then rinse with water first.