1) Am I damaging my fridge by keeping it on?
Depends what temp the garage drops down to.
If you get too far below freezing you are not doing it any good.
Compressor has oil in it which thickens with the cold and can make the compressor work harder to get started.

The fridge section seems to stay cold enough.
Your problem is the defrost. The defrost heater comes on putting heat in the freezer section but due to the ambient temp the fridge does not come on after defrost so the heat melts your food.

2) If I want to use the heat of a very low watt incandescant bulb (<15W) to fool the fridge into working...where would I put it? Near the exhaust?
Up close to where the end of your thermostat capillary is

Problem is you will have to check the bulb regularly. If it burns out you are back to your original problem. Might be better off with 2 small ones. You may have to move it around as you are trying to do a balancing act between the bulb's heat and the fridge's set temp.

Cannot really help but get your Model Number and go to the Sears or Kenmore site. Go to the customer service area and see if you can download a parts breakdown for this unit (sometimes is in the manuals section).

You may have to sign up for Manage My Home site which seems to be down as much as it is up and running.

Kenmore's are a pain to get any useful info on re: wiring diagrams, parts layouts etc.

If you do not have a wiring diagram for it, take a look behind the kick plate they may have hidden it there. May even be taped under the drip tray.

If the unit is thermistor/ PC board controlled it may be difficult to do this mod.

Thermostat looks like it is mounted under the cover on the top of the fresh food compartment.

Looks like the capillary goes to the rear of the unit where there is the vent which connects the freezer to the fresh food. May go up through this vent.