You have a moisture problem somewhere. The light gray patch is portland cement and it’s making the problem worse because water vapor can’t pass through cement. It condenses back into liquid before it escapes and starts dissolving your bricks. Old fashioned lime concretes and a mortars have almost no cement in them and the old fashioned mortars allow water vapor to pass through. The problem is made worse because lower quality bricks were used on the back of rowhouses, saving higher quality and money for the front.
Find the moisture problem. It might be the chimney, make sure it’s venting properly. I’ve seen chimneys plugged up (by accident and on purpose) and the result is that hot wet air condeses like crazy inside the chimney than soaks into the brick. Remove any cement patches. They’re making the problem worse. Remove any loose paint (flakes, blisters, etc.) some paints aren’t compatible for brick the same way cement isn’t, the paint traps moisture. Look for bad roof flashing at the top of the wall. If you parge with stucco, no need to look for holes in the mortar, they’ll be covered up anyway.
Then parge the wall with a coat of lime-based concrete stucco, keeping cement content to an absolute minimum. A good parging of stucco should last 20-40 years as long as you do all the prep work explained above. If you skip the prep work the stucco will be lucky to last 10 years and the brick will be even worse than it is now.