My children had foreign further education and initially stayed with host families till they settled in and found the area they wanted to live in independently. Some of whats being said here I understand but other things have left me feeling very down hearted. Its a mixed bag really. There's quite a few snide references/pre-conceived ideas going on whilst others parts of it are good and I imagine the girl and her family are capable of the same. Hopefully though at the end of it all each will have different notions going on about a lot :)
My children would have been the gadabout type because thats the way they are, they also had previous UK exposure. My nieces who are currently at University in the Uk would be the gadabout type because they're outgoing girls (and practising Muslims), but their wee school friend who's there also would be like the quiet girl in the OP. Its just the way she is. Maybe the quiet girl in the OP is just horribly homesick and too much is being made of other things.
The girl with my niece's isn't downtrodden and like my nieces is studying for a career that is usually male dominated world wide. My other niece also has a PH'd in the same subject and Im going to assume the it was just tongue in cheek when the Op said about families being able to educate kids abroad - 'girls even'. I don't know a family that isn't hungry for their daughters to be educated, even at great private expense, because the days of scholarships for all are over given the education now available in their home countries and the chances are that if a youngster is studying abroad - their parents are covering the cost. Most of them are not loaded - they just make sacrifices.
And just as as point of interest the girls in my family have the following careers:-
2 Doctors
2 Teachers
2 Bank Managers
3 Geologists, including one with a PHd and the rest with a Masters.
4 Business women who run very successful businesses and are all educated to Masters Level in Business.
2 University Lecturers, one with a PHd in Chemistry, and the other with one in Physics.
1 high ranking Government official in her chosen field.
1 SAS trained bodyguard to a VVIP
Re would it be unreasonable to suggest she doesn't wear her Abaya when she goes out? Yes, it would be. I do however understand why you are thinking the way you are.
The Marmalade, maybe she's tried it and didn't like it. There's plenty in the shops in this part of the world to chose from so I would just give the Strawberry Jam because its also a British thing and there must be many a house that doesn't bother with Marmalade so its not really a 'must try'.
Not being allowed in the house between 9am-5pm. This is one I will never understand and wouldn't have stood for it for my children, but luckily I never had to. They are not criminals or deviants and would have been Ok left alone in someones home. I would imagine this girls the same, but maybe because she prefers to be at home, and for that reason only - perhaps a move to another family who allows the students to be at home during the day would be better for her.
Friday is the Islamic equivalent of the Sabbath.
How to help the student settle in? Maybe get in touch with the nearest large university and see if they have a Students Association from her home country and get her hooked up with them. They have outings etc and it may just be that she finds herself a pal to go places with, or visit.
I hope this has been of some help to you. :)