Forgery has a
specific legal definition and refers to the counterfeiting of documents. At the core, the forgery is an imitation -- it tries to look like something else. Etymologically, it does come from its obvious origin, the forge, and so refers to craftsmanship. You can forge a letter, you can forge an item, but you cannot forge something more abstract such as a coup. Example:
"this signature has been forged!"
Staging refers to the theater. There's a lot of things that you can stage, though. At the core, the idea of staging is to arrange things such that they will be able to proceed in the desired manner, which makes it a quasi synonym to organizing. So this is the opposite of forgery, in that you cannot stage an item, but you can stage a process. So you can stage a coup, a revolution, or whatever, which makes it a word of choice for fans of conspiracy theories who see false flag operations everywhere. In other contexts, you can see staging used for things such as the placement of tools and materials in a factory to allow efficient production of something; the placement and movement of aircraft in an airport so that they can load and unload their passengers and cargo quickly, move to their runway without traffic jams, and take off without colliding with other aircraft; or the design and process of rockets by which several elements (appropriately called stages) will work then detach so that the upper stages can replace them. Remember Doom 64 MAP01? "Staging Area"? That's the area where you organize personnel and materiel to sustain an operation. Example:
"these protests were staged!"
Fixing, etymologically, is to put something (that broke loose) back in its place, and hold it steady. This notion of position, of something that will not move, can be seen in words like prefix or suffix (since we're talking language), fixture, or fixed point. In common parlance, to fix something is to repair it, hence expressions like "it it ain't broken, don't fix it" or "fix for bug #42069" or whatever. By extension, it means making sure that a process will yield the result you want (instead of the natural result it could have had without interference). In that sense, a synonym is "rigging". Example:
"these elections were fixed!"
In short: you forge an
item, you stage an
event, and you fix a
process.