My mother-in-law is from Afghanistan and is 72 years old. She has lived in the U.S. for seven years and wants to apply for U.S. citizenship. Her health is good, but she received very little schooling growing up, and she now has a great deal of trouble with speaking English and therefore also with studying for the civics exam. As far as I can tell, she doesn't qualify for any age or disability waivers – is there any way she can be approved for citizenship?
At the very least, your mother-in-law should qualify for what is called "due consideration" when applying for citizenship. Under regulations written by U.S. Citizenship and Immigration Services (USCIS), the officers interviewing people for naturalization are, when choosing test questions, phrasing their own questions, and evaluating responses, supposed to give due consideration to the applicants' "education, background, age, length of residence in the United States, opportunities available and efforts made to acquire the requisite knowledge, and any other elements or factors relevant to an appraisal of the adequacy of the applicant's knowledge and understanding." (See 8 C.F.R. PART 312.)
This doesn't mean that the citizenship examiner will skip over the English or civics exam. Your mother-in-law will still need to pass both of these. (That's assuming she indeed doesn't qualify for any waiver – doublecheck this in the "Waivers for Age or Disability When Applying for Citizenship" section of Nolo's website.)
But the officer should try to make it as simple as possible for the applicant to pass. For instance, when asked to write a sentence, the applicant should be given a short, easy sentence, and the officer should overlook any spelling or punctuation errors that don't interfere with someone's ability to read and understand what's written.
Given what you've described, in particular your mother-in-law's age and educational level, it sounds like she may well merit due consideration from the interviewing officer.
What you haven't mentioned, however, is what efforts she has made to gain the required knowledge. It might be worth looking into whether classes in English as a Second Language (ESL) and citizenship exam preparation are available at local adult schools, and have her attend, if possible—at least to show USCIS that she made an effort. (If you don't find any appropriate classes, make a record of where you checked and why nothing worked, for purposes of showing the lack of local opportunities.)
The next step is to prepare an actual letter in which your mother-in-law explains how her situation fits the USCIS regulations and requests due consideration in USCIS's administering of the exam.
This letter is important – USCIS officers do not automatically give due consideration. (In fact, sometimes they don’t even give it when they're supposed to — the agency is notoriously inconsistent in this regard.) You or an attorney can prepare this letter, explain it to your mother-in-law, and have her sign it. She should then submit it with her Form N-400 Application for Naturalization and bring a copy with her to the interview. If she has already submitted Form N-400, it's okay to bring it to the interview anyway.
For more information on the naturalization process, see Nolo's articles on "How to Become a U.S. Citizen" and the book Becoming a U.S. Citizen: A Guide to the Law, Exam, and Interview, by Ilona Bray (Nolo).