No, TurboTax does not do anything in regards to any residency issues, which is why I usually recommend a tax professional. However, in regards to paying Social Security and Medicare taxes, that is something the employer does, not TurboTax.
For what purpose are you asking about being a student? The college makes the determination for what is called "full-time", but for tax purposes, the student usually must be a student for parts of at least 5 months to be called a full-time student. If your wife was only in school for parts of 4 months, she probably would not qualify as a student.
