The thing on lower left corner on picture 1 and 3 is AC compressor. Lot of people disconnected the belt to the compressor assuming that it is taking lot of fuel to run it, but in my years in CA I never noticed any mileage difference between AC season and heating season.
On some engines that belt double as a drive for water and radiator fan, so it is good to have it in such a case even if you are not using AC.
Judging from the look of the compressor it might be hard to restore it, not to mention that you'd probably have to convert the system to 134 freon.
Good luck.