Grad Student Taking a Car to California--Questions

I have known plenty of OOS students in CA who have never had a problem, not to stay that your DD won’t be asked, but if she has an OOS car and an OOS driver’s license she ought to be ok. Her being a student or not, income, rent, etc. is not likely to be asked by the police pulling her over.
When life is complicated choose your story and be consistent, either she is or is not a resident of CA and everything she does should hang on that fact.

Another question will be income taxes if she has taxable income, CA forms will ask how many days she spends in CA each year, so year one fall and year two spring are fine, but in between she may be a tax resident if she has income