I agree that the condition of your wall and your lack of plastering skills warrants calling a professional. Have you checked the R-value of the 1" insulation? Is your attic fully insulated and all holes filled to preclude the stack effect? How old is your home? I'm in Western PA, and found having the attic and garage ceiling professionally insulated made a massive difference as regards my utility bills.

@ceilsan32 We live in a row home which does not have an attic. This wall is one of the few that is exterior facing, most are party walls. The home was built in 1920. The 1" insulation board is r-value is 5.

Unfortunately, the R-5 won't be of much help. You might consider adding reflective foil insulated panels on the wall area behind the radiators, having insulation professionally added between the brick and interior walls (done from the outside, through mortar joints, then mortar is rematched), evaluating the cost of replacement windows on this wall, or adding exterior mount double rods and heavy duty draperies with a thermal liner behind them. Do you have a heavy rug with padding and heavier duty fabrics on furnishings in this room to avoid the room being too cold?

@rwiegand , in the parts of the wall which expose bricks, it doesn't look like they are in good condition. in fact, when we tap at one part of the wall, a fair amount of brick dust pours out. I am sure it'd be hard for you to assess the situation without seeing it in person, but do you think we should remove the plaster purely to inspect/repair the wall? Aware of course of the can of worms that might be opened, it does sound nice to have a plasterer seal it all in. thank you for your response!

@ceilsan32 the room is not too cold to be honest. I suppose I am just asking whether to insulate given that we have the opportunity to while proceed with the wall. I am sure new windows eventually would do more than 1" foam insulation!

I think you need a plasterer and/or mason to inspect the wall. Old mortar does degrade with time, hence the periodic repointing of walls on the outside. If there is degradation on the interior surface that threatens structural integrity then you need to attend to it. If it's just at the surface you're probably OK for another century or two and should just plaster over it. The places where the plaster has already fallen off are probably the most likely to be unsound, so they are probably a good place to look.

I agree with rwiegand that a plasterer should be able to best tell you if installing the foamboard would help, but it also sounds as though replacement of mortar is warranted.

Make sure you contact a number of mortar repair companies, if needed, because the cost difference can be more than several thousand dollars, dependent upon the degree of work involved. Also ask for a written warranty on any work performed.