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If she wishes to come here to study then she must apply for and obtain a student visa. She must receive an offer to study from a university licensed to sponsor foreign students (most mainstream universities are). This is a points based visa, so she will have to meet the required number of points, it is quite restrictive and expensive I'm afraid.
You can check her points eligibility and other requirements of eligibility here:-
Depending on the qualification she is studying for she will either be able to work 10 or 20 hours per week.
In order to naturalise a person must have a period of residence in the UK, they must then apply for what is called Indefinite Leave to Remain and then apply to be naturalised.
There is no special provisions made for students in respect of applying for ILR so any application made would have to be under the long residency rules which requires a 10 year period of unbroken legal leave to remain in the UK. Obviously, her course may not last the ten years so at the end of it she would have to switch to a worker category.
Having English grandparents helps in this respect in that she will be eligible to switch in to a Ancestry Visa subject to meeting the eligibility requirements on this page:-
Indeed, she could apply for an ancestry visa now if she wishes but she would have to intend to work full time and not study.
Once she has been on her ancestry visa for 5 years she could apply for indefinite leave to remain provided she has not spent much time out of the country. Once she has ILR she can apply to be naturalised as a UK citizen 12 months after receiving ILR provided she meets the following criteria:-
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