yes, now please either do something about the spirit, I have given you all my advise, if you are not satisfied then you may go to a moderator or a contributor, I bet they will have some advice.
A ceiling fan is typically bolted in place. If it comes loose while on, it is because the bolts vibrated free of their fittings and it fell.
This is far, far more likely than the physical manifestation of a spirit.
This is not to say that the spirit you dreamt of is not real. It is possible she is. Banishing rituals and the like will only work so far if you continue to think of her. Keeping her in mind is like opening a doorway that allows her to come back, or at the very least like providing a window for her to look into.
Work your banishing rituals and then find something to distract yourself. A funny movie that makes you laugh. Conversation with friends. Etc. Laughter and smiles are the best for putting such things out of mind.
If it wasn't attached to the main beams that run through the ceiling (the exact word for them eludes me right now - living up to the screen name again) then of course it fell down when it was running, and when it did so the wires snapped. Sheetrock and other ceiling paneling doesn't really support those things.
It sounds like this ghost is trying to get your attention. Instead of freaking out and feeding it more negative energies, try figuring out what it wants. You have gotten lots of good advise but you have not said what you've done with it. Has she thrown more than the fan, if so what? Document every thing. Do not be afraid of her they more than likly wont harm you. Before you go trying to get rid of it try to figure out what it wants.
When I first saw a spirit in my room I placed bags of salt next to my bed and in the areas where the spirit had appeared. It's typical that they come to you in dreams, the same happened to me.
Since I can't sense the spirit from where I am, I can't tell you if you should try to talk to her or not. Maybe you should try to feel if you really think the spirit is malevolent. Maybe she just wants attention, or is upset. I don't know if you should try to talk to her, in case she is demonic. You could try to use a spell to set her free, or a banishment?
