Possibly a handyman. The main thing is to make sure whoever does the work is competent - it's not easy to clean up spray foam or caulk off of the brick. It pays to do a nice neat job from the get go. Many painters can do the caulking, not sure how many would be willing to apply the spray foam. I assume the low expanding foam would be the type to use.

To answer your questions, no it doesn't usually hurt anything to leave it as is. Although a couple times I have seen some with so much water in them that they could be used as an aquarium for fish. You have to replace both pieces of glass, which together form an insulating glass unit (IGU). If you can't identify the mfg and order one from them, or on warranty from the installer/mfg, you will need to order one at a commercial glass shop. If you can take the sash to them it will make their job a lot easier and probably less expensive for you. Sometimes it isn't possible to match the color of the low-e glass in some of the older windows exactly.

There are no markings that I can find other than an inspection sticker. I wondered if there might be something hidden somewhere. I understand that both pieces of glass have to be replaced- I was asking if both the fixed window and the movable window have to be replaced. Maybe I am not looking in the right places but I don't see that I can buy just the half I need. As for the matching, I was more concerned about the color of the white frame around the glass, not the glass itself. I hadn't thought of just removing the window and taking it to glass shop. I suppose they could take a couple quick measurements and order what I need. The window comes apart easily enough that I could put it back together while I wait for the new one to arrive. Anyway, I measured and was ready to get something shipped to me but I don't want to buy the entire window if I don't have to. I only want to replace the fixed window with the bad seal.