Thats a good one! lol .
Problem 1:) You said when you plug the garbage disposal into the GFCI , it trips it. Right off the bat I imagine the garbage disposal windings are grounding out somewhat on the frame of the disposal...or your sink...., thats my guess to that? Either way if you have an electrical meter you can test this with the disposal unplugged and your DMM in resistance (ohms) mode.
Problem 2: The outlet doesn't work with a normal item plugged in. If your sure said normal item is good, then something happened to your house wiring, this concerns me. The breaker should have caught anything before wire damage took place. If you had a short, your breaker would be tripping. But I don't think it is from reading your story? So the other options are this, your breaker isn't resetting? Or you got an open wire somewhere, or the contacts in your outlet burned out. Whatever happened, it really shouldn't have with modern house wiring with all the components sized correctly. Idk how good you are with a meter, but this is definitely something you can trace down if your the kinda person who enjoys a challenge. Somewhere, something is wrong... I know that sounds over simplified, but really, with an electrical problem it can be traced down with just a few measurements, usually.