Plug a multi-outlet adapter into a GFCI outlet

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.

Any equipment that uses a two prong plug will be as safe being plugged into this setup as they would be if they were plugged into a properly grounded three prong outlet. Two prong plugs (obviously) do not use the ground pin. As for three prong plugs, this depends on what is being plugged in. If the item is a laptop power supply that is sealed in a plastic shell, the ground pin is pretty much ISO-proforma [meaning, that is the standard cord- whether the equipment needs a ground or not.] I would be hesitant to plug in something with a metal shell, like a full size desk top tower, because the power supply is enclosed in a metal shell and attached directly to the frame of the case, this could present a shock hazard if the power supply were to malfunction.

A GFCI is a good start. If they are functioning properly, they will guard against lethal shocks, but you may still get a tingle if the electric is not quite right.

A possible suggestion: Use a 2->3 pin converter and attach a ground wire to the grounding tab. Attach the other end of the wire to a radiator if you have steam heat or possibly a metal water pipe. (no gas pipes.) This will get you a ground and you can use those items safely.