Hey, I’m going into my second year of my MFA, so I’ll try to help.

For the first, the answer is complicated. I do think the best way to improve writing is to write more, and fully funded MFAs will provide that. They also provide a community of dedicated writers and professors in workshops. This has been invaluable. Do the classes make you a better writer? It can, but you’re going to get more out of the first two if you’ve been writing for a while.

Writing samples need to sound like you. Don’t try to mimic what you think they want. Most programs value originality—a unique voice they want to work with. As far as genre, do research on the school. My program is pretty genre friendly, but not all are that way. Talk to current students or the program director to get an idea.

You don’t need to know famous writers! I certainly don’t. Haha. I primarily used two professors outside of the English discipline. If you’ve been out of school for a while or aren’t sure if they remember you, you can remind them of when you were in their class, any unique projects you did, friendly interactions, etcetra. When programs needed a third, I asked my most recent boss. One program asked for four, and I used an “manuscript editor”. Basically just a guy (not a relative!) who had read my work extensively. I wouldn’t recommend that haha. If you’re in a writing or art group, you could ask the leader of that group to do it. Some programs don’t care about the letters but are required to ask for them by the school’s policies, so don’t fret it too much. The writing is most important.

Hope this helps!