Quote: "When I opened up AppGameKit, it asked me to set a default location for projects"
This is triggered if the location "C:\Users\<username>\AppData\Local\agk" doesn't exist or is corrupt.
Quote: "When I tried opening up my project, it was empty"
I don't know of anything that could cause this, but I don't know the Geany IDE that well. Given that the above happened then it's possible it couldn't read the file properly, so showed an empty document, but still managed to write this empty document when the IDE was closed, but I can't be sure. If this happens again then as soon as you see the empty document in the IDE, Ctrl-Alt-Del and end task the IDE so it doesn't save the empty document.
Quote: " Is it possible to somehow reverse-engineer the windows executable to show the code?"
Theoretically it's possible, but it would be very difficult, and probably look nothing like your original source code.