Ogre covered it pretty well.
I just want to add that unlike some writing sites, this site highly discourages publishing 'chapter by chapter'. In fact, doing so is really not the standard or the expectation. Unpublishing and republishing a story will also mean it no longer shows under the new games section, it will also retain all comments (which means the comments may be misleading if you changed a lot). Demos are also almost always disliked.
Here it is highly encouraged to published finished works.
With that said, if you want feedback or to share an incomplete storygame, there is a sneak preview option under storygame settings which allows the storygame to be accessed without being published. If you actually want feedback when doing this, it is a good idea to make a thread in the Writing Workshop so that people know you actually want feedback (as sneak preview is on by default).
You can also just ask general questions if you don't have anything you wish to share, but keep in mind this can make the feedback more generic and potentially less useful. Really depends on what you are looking for.
HOWEVER if you want to work on something with parts, it is doable (just look at Homo Perfectus [author profile]). This can be quite the undertaking so it is generally not recommended if you are new to branching narrative writing. You would also want each storygame to be able to stand on its own (in some capacity at least).
Also, adding additional things to a storygame after it has been published can be done, but it is tricky (just look at Eternal), I wouldn't recommend trying to do this tho because of all it requires. However it is technically possible if you have a specific goal.
I'd recommend just sharing WIP's with the sneak preview feature, as this tends to require the least work (since you don't have to finish anything, since to publish you need a complete storygame [unless you want it taken down]). Since you seem to have written something already but not finished it (the fanfic) this is the option I recommend.
Anyhow, welcome to the site!
