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[Harry Potter] How do the ghost mechanics of the Potterverse work? For example; how does Professor Binns check homework?

Ghosts of the Potterverse confuse me a little and I was hoping there may be some logical reasoning to how some of the mechanics work.

1.) So students are assigned essays in Professor Binns class.  When they turn in the homework, how does he check it? Meaning; while a poltergeist is able to have an effect on the physical world, a ghost can not. Who unrolls these parchments for Binns to read? Is there maybe an aide that we don’t know about?

2.) Nearly Headless is telling the trio about receiving a rejection letter from Sir Patrick. The letter is a ghost letter...  how was this letter written, delivered and received? 

3.) Are ghosts bound to one specific place? We see the headless riders visit, but could Nick leave the castle at some point and travel to America, if he wanted?
gpt
1) Ghosts can interact with the physical world, just not to the same degree as poltergeists, remember Moaning Myrtle repeatedly floods the toilets in her bathroom. Or it's possible that binns as an assistant or some sort of spell active that allows him to grade their work.

2) Again ghosts can interact with the world, so it maybe an actual letter, or it's special ghost paper.

3) Seemingly no, the gray lady and the bloody baron both died in *Albania, NHN was beheaded in a muggle kingdom. Clearly the are able to move around if they could return to hogwarts, to what degree is unknown; generally Ghosts end up being restricted to place that they had been while alive.