You're going to have to inspect each junction and device in the circuit, starting with the first know bad device. It sounds like you have a GFCI in the house, which feeds a receptacle in the shed, which in turn feeds a switched light in the shed. Since the receptacle in the shed is the first know bad device, you'll want to start there.
Turn off the power at the circuit breaker. Pull the receptacle out of the box, leaving the wires connected. Inspect the wiring for loose connections, and fix any found. If there where no loose connections, you'll want to determine which wires entering the box feed the receptacle. If this is not obvious, you'll have to do some testing. For this you'll need a multimeter with a continuity function. Disconnect one of the neutral (White) wires from the receptacle, set the multimeter to test continuity, touch one probe to the equipment ground, touch the other to the disconnected neutral, then to the still connected neutral. If one tests positive (audible tone, or reading on display), that is the feed line. If neither or both test positive, you'll have to do testing with the power on (which I won't cover here since it is unsafe, and you should call an Electrician at this point).
Now that you've found your line wires, reconnect the neutral to the receptacle. Leave the receptacle out of the box; making sure nothing is in contact with the edge of the box, then turn the power back on. Turn the light on in the shed. If it goes out, use a non-contact voltage tester to test for voltage. If you have voltage on the line but not the load, replace the receptacle. If you have voltage at neither point, run similar tests on the GFCI receptacle.
If you have voltage on the load side of the GFCI, but no voltage on the line side of the receptacle in the shed. You'll have to inspect the wires connecting the two devices. Start by shutting off the power, at the breaker. Next disconnect the load wires from the GFCI, and the line wires at the receptacle. Run a continuity test between all combinations of the wires, none should test positive. Finally connect one pair of wires at one end (so in the shed, twist the black and white wires together), do a continuity test on the other end to make sure the circuit is not open.
If all of this has been done, and the problem persists, you'll want to contact an Electrician.
As always, if you don't have the proper tools, or you don't feel comfortable doing any of the work mentioned. Do not hesitate to contact a local licensed Electrician.
Answers in order:
1) If the kitchen was done properly in the 90's you definitely should have GFI protection, at least near the sink(s). If not then yes, you cetainly can install a GFI at the head of the circuit and protect downstream standard receptacles.
Keep in mind, only receptacles serving countertop areas require GFI protection.
2) IF the house is that old GFI protection was likely not required at the time of original installation. You can if you like add it at any time, and it's the same situation as the kitchen. Downstream protection is fine.
3) See answer #2. I doubt there is a need for an actual GFI device behind the freezer.
4) Again, same goes. You can just use one GFI at the beginning. As for how many, there is no limit, but each downstream device does have a tiny bit of current leakage, so limiting them to 5-6 is a good idea.
Remember, to gain downstream protection, the incoming line must be on the LINE terminals, and the line to be protected must be on the LOAD terminals.
Best Answer
Is there any benefit to tripping a GFCI receptacle when it's not in use?
Does big current draw make GFCI outlets go bad?
I'd say you're over-optimizing. You only need 1 GFCI outlet on a circuit, and it'll last about 10 years. That's around $2/year. That's if GFCI outlets degrade from simply being attached to power; the second linked question indicates that heavy loads and similar usage causes the wear and tear.