Following up on an email to a potential adviser for feedback on research proposal? 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?
When to email somebody a follow-up email depends on how time-sensitive the topic is and other factors you may be aware of.  For people in close contact (e.g. a student taking a professor's class, or colleagues), a day or two is typically an acceptable wait time. For somebody that you initiate email contact with, a week is more typical. Other considerations are how much thinking the response might require: if you asked lots of questions, they may need more time to think about it before formulating a reply. Do you have reason to believe the person may be busier than usual (e.g. exam season or a conference)? If so, it would be polite to give them more time to catch up with their email. 

In this case, a week or two is probably a sufficient amount of time. Less than a week would be too soon, as you haven't met them before emailing them. More than two weeks is getting close to winter break, at which point most academics check their email less frequently, and you need enough time to contact other professors if she suggests any. It's also possible other people are asking her similar questions. It's a busy time of year, so one follow-up couldn't hurt. (If she doesn't respond after a second email, I wouldn't send a third email.) 

Here are a few resources you could check out about how to write your follow-up email: 


How to write a polite reminder email? 
How to remind a professor about sending papers to read?


You'll find other resources linked from these questions and by searching online, too. Most formal reminder emails follow a similar format. Remember to be brief. 

It's certainly worth contacting other professors! I do not see any reason why not to.