Electrical – Why is the GFCI/Switch combo working in such an odd way

Ok I read your question a few times, so hope I understand what you want to do. You want GFI prtection on the outlet , but no GFI protection to the fridge. This will be easy to do if you can affirm that the load wire leaving the j-box where the switch and outlet are located, is actually the feed for the fridge. To check this out, you need to turn off the power, check the outlet at the sink and fridge to be sure they are ,in fact on same circuit and off. Now disconnect all the wires from the outlet and any wirenuts so everything is isolated. Now, carefully turn the power back on and check the hot (typically black) leads to ground with a volt meter to determine which one is the feed/source wire. Mark this with some red electrical tape. Double check to see that the fridge outlet is still dead.

Next, turn off the power and wire nut the black source wire and associated white neutral to the black and white wires you suspect goes to the fridge.( black to black, white to white) Turn the power back on and check with your voltmeter at fridge outlet again. If there is voltage there now, you have found the right feed wire to the fridge outlet. An alternate method of finding that wire with the power off, is to use an ohm meter. Assure the power is off, then twist the black and white together on the wire you suspect goes to fridge and check the hot and neutral slots of the fridge outlet with your ohm meter. the meter should show 0 ohms or "short circuit".

Now that you have identified the hot feed and load wire to fridge in your box, you can wire it so only the counter outlets are GFI protected. Put the source black wire together with the fridge black wire, along with a separate 8 inch piece of black wire (pig tail) and wire nut them all together. Use the 8 inch black wire to feed your switch/gfi hot. The neutrals tie together as usual with an extra pig tail for your GFI outlet neutral. Obviously, trim the pig tails to a comfortable length to fit in your box before connection to the GFI.

Since all outlets must be GFI protected in the counter outlet and since you cannot split a gfi outlet top and bottom like in your diagram, you have to do your light differently from your previous plan. I would suggest using a switch/single outlet device wired from the load side of the gfi. Wire the switch in series with this single outlet. This means only the single outlet is switched and gfi protected. You must have gfi protection on this outlet, as someone could unplug the lights and use it for something else.

Hopefully, one of my artistic buddies can do an edit and add a nice diagram depicting what I have outlined for you.

You have some pretty weird wiring to the light fitting. It looks like at the light fitting (fed from top-right romex at box) you would find

• the "ground" wire (green or bare copper in the US?) is being used as a neutral return from the light bulb.
• the "hot" (black) is a switched hot to the light bulb.
• the "neutral wire (white) is being used as a permanent hot for some other purpose.

So I'd expect an ordinary light fitting to be using the false "ground" and switched hot wires only.

The permanent hot (false neutral, white) might have been used (now or previously) to power some kind of device that needs live power. For example a remote light control or a ceiling fan that is operated by a pull-cord independently of the light bulb itself.

I would check the wiring in the light fitting controlled by that switch. Then I'd label the wires at each end to make clear what each wire is really used for. Alternatively, you could rewire it properly - that would be best if the light fitting is a normal conventional simple light only. I'd double check that something else (an extra outlet?) isn't already wired from the light fitting end - disconnect the white wire from the three black and see if an outlet or something stops working.

If you can't figure it out it might be best to call an electrician.