American High School --> UK University

I am a dual American and British citizen -- I was born in England in 1967 to a British father and American mother and have lived most of my life in the US.  I have a 14 year old daughter who is going into 9th grade (freshman year in a US high school).  She gets very good grades and has expressed interest in going to university in the UK when she graduates high school.  I have read about the application process for UK universities and we can focus on her taking the necessary classes and AP tests, etc.  My questions:

1) It's my understanding that my daughter is a British citizen also, being born to me as a British citizen despite being born in America (my wife is American solely).  We have not applied for a British passport for her.  Do you think I am correct about her citizenship?

2) If she is a British citizen, but has completed her secondary education in America rather than in the British system, do you think she has an advantage in getting accepted over other international candidates? 

3) Do we stand to pay lower university fees as a British citizen than as an international student?  Keep in mind I have not paid British taxes at any point.  Is there an equivalent to "in-state tuition" as we think of it in the US that would be available/applicable to us?

Thanks in advance for any insights! 

1) It's my understanding that my daughter is a British citizen also, being born to me as a British citizen despite being born in America (my wife is American solely).  We have not applied for a British passport for her.  Do you think I am correct about her citizenship?

Yes, as long as you were born in the UK to UK citizen parents (and therefore you are a citizen 'otherwise than by descent'), then your daughter has been a UK citizen since she was born. All you need to do is apply for a UK passport for her.

However, because she was born in the US, she is a UK citizen 'by descent' and therefore cannot pass her UK citizenship down to her own children UNLESS those children are born in the UK (or if she marries someone born in the UK and then they can pass their citizenship down to them).

2) If she is a British citizen, but has completed her secondary education in America rather than in the British system, do you think she has an advantage in getting accepted over other international candidates? 

No, unfortunately not. She will need to meet the same international student entry requirements as everyone else. On the plus side though, she won't need a visa to study in the UK.

It will depend on the university and the degree programme, but she will generally need either:
- AP classes (level 5) in subjects related to her degree program (in the UK you choose your major before you apply),
or
- US college level classes or a US Associates degree

3) Do we stand to pay lower university fees as a British citizen than as an international student?  Keep in mind I have not paid British taxes at any point.  Is there an equivalent to "in-state tuition" as we think of it in the US that would be available/applicable to us?

Unfortunately, even though she is a UK citizen, she will have to pay the higher international tuition fees.

She won't qualify for UK/Home fees unless she has lived in the UK/EU for at least 3 years before the degree course starts (this also applies to UK citizens who were born in the UK and grew up here, but have been living abroad).

UKforMe? Thank you for asking that question because it's been on my mind too. My daughter was born in England but has lived for 12 of her 15 years in the US. My husband and I want to return to the UK when she graduates in 2019 and she's already preparing to take her classes leading to AP.

Thank you Ksand24 for answering the questions set forth regarding "international fees". It's not the best news to learn that my daughter doesn't qualify for the lower fees despite being a UKC but it is what it is...