Are there any language requirements for citizen applicants with low English skills? I see from a university website that "if you are not a citizen of one of the following countries..." [a list of countries], "you will need to take the TOEFL before enrolling."  (USA is not on the list, but I presume that's irrelevant).  My friend is a US citizen originally from a different country, and her conversational English is passable, but she absolutely would not pass the TOEFL.

In most schools, could she walk in without the test, because she's (lately) obtained her US citizenship?
Usually, universities set the requirements by native language and/or educational experience in English. If you have a bachelor's or PhD from a US university, they usually waive your language testing requirement because (1) you probably have already passed one many years ago and (2) if you're not good enough at English you probably would not have received your degree. 

But if you're just an American citizen, no. They don't usually waive TOEFL just because of your passport. There are many Americans out there who don't even speak English. Of course, if you're an American citizen whose native language is English, you would most certainly not be expected to tale the TOEFL.