Advice for insulating old brick building?

[Ryan Redenius]

I recently purchased a 3 unit building in Chicago.  I'm occupying the basement unit, and in my unit along an exterior facing wall are all of my pipes controlling water for the 3 units as well as the main.  These pipes are all type M copper, which has already resulted in a pipe burst last week, and I'm getting them replaced with type L copper along this wall.

Upon opening the wall I realized there's zero insulation, which makes sense because it's always cold in the living room.  Since I'm doing repairs after the pipe burst and need to open up this wall anyway, I want to add insulation to it.  However, I've read to proceed with caution when adding insulation to old brick building (100+ years in my case) because it can result in freeze/thaw damage due to increased moisture, rotting joists and beams that are embedded into the wall, etc.

I believe one of my upstairs units along the same wall is lacking insulation as well, which has resulted in frost in the drywall on really cold days (see attached pics).  I want to get this fixed, as I'm sure it's driving up my tenants heating bills and could lead to increased vacancy in the future if they're too high.  I am told that upgrading the pipes in my unit along the exterior wall will help a lot against future pipe bursts, but it's extremely drafty inside the wall, so I'd feel a lot better adding insulation.  Does anyone have advice on the best way to go about this?

Thanks in advance.