The graduate program to which I am applying has a centralized admission procedure, so individual professors cannot accept students. However, they recommend taking a look at the faculty, so that our research proposals are aligned with the work being done there. (Un)fortunately, the field I'd like to work in is quite unexplored, which might help me — but also makes it hard to find professors with a similar interest.
While browsing the faculty Web site, I found the professor whose research aligns most with my intended research proposal and whose page explicitly encouraged potential students to get in touch, so I emailed her to ask if (1) she thought our interests would be compatible and/or (2) she thought that someone else in the department could be interested in following me. It was a thoughtful email, a brief introduction and references to her previous work. It's been a week and she hasn't replied yet — and with professors I've learned that if they don't reply within a day, they probably missed your email, or they saw it but forgot it immediately after.
I really would like to follow up on my email, because the holiday break is approaching. I'd really like some feedback on my proposal before I submit it in early January. I also think that showing that I got in touch with the faculty would help my application. However, I also don't want to seem too insistent, because it might hurt my chances. Should I email her again? How long should I wait before I do so? Or maybe she did not reply in the first place because my email was inappropriate?
Also, there are a few other professors who might be compatible with my research proposal. Would it be good etiquette to email them too?