I would automatically assume that there is probably not any insulation in the walls. If there is, it is probably vermiculite granules which settle over time, leaving a large void at the top of the walls. This was somewhat common in that era.

The easiest way to see what type of insulation may be behind the walls is to find an outlet or switch on the outside wall and remove the cover plate (be careful you do not get shocked turn off the power to the device) and open a small area next to the electrical box within the area the cover plate covers and look into the wall. To learn quantity and location of the insulation there is, the thermal image camera we use during a home energy audit will reveal the answers.

For the second question: retrofitting insulation into the walls of a structure such as yours is not an easy task. Best case scenario: you remove the wall coverings and insulate the walls then replace the coverings with drywall. Or, drill a large hole at the top of each cavity and have blown in insulation installed: they will stuff the tube for the blower down into the wall and fill the cavity as best they can. There is no way to guarantee they can fill the cavity completely and if mid point blocking is present it will then require a 2nd set of holes to fill the cavity. Then you have a ton of patching ahead of you with questionable results.

If you are not willing to, basically, rehab the inside of your home, I suggest these tips:
1: insulate the attic normally, and make sure it has proper ventilation
2: upgrade your HVAC system to a sealed combustion, high efficiency unit, and don’t for get to do the same with the water heater.
3: tighten the exterior of the home by caulking windows and doors, seal around penetrations like light fixture boxes, dryer vents, etc.
4: tighten up the interior by installing insulated barriers on electrical devices and other penetrations on the exterior walls.
5: insulate the ends of the floor joist cavities in the basement.
6: replace old single glazed windows with newer thermal windows (if your existing windows have sash weights DON’T FORGET TO INSULATE THE WEIGHT CAVITY).

By sealing everything up you minimize air infiltration and gain some R value buy creating a dead air cavity inside the walls. This can be a double edged sword however. It is very possible to make a house too tight. If the house is too tight the indoor air quality can suffer creating carbon monoxide hazards, mold issues and other undesirable results. There are serious safety concerns with over tightening your home. This is why it is so important to begin with an energy audit, because it reveals exactly where the problems are and provides the safest and most effective solutions.