I have never before lived in the UK and am a first generation American with the ability to acquire dual citizenship. I’m looking into going to college in Edinburgh or London (both in the UK), and am wondering if having citizenship would get me the less pricey tuition of citizens of the EU and the UK. For example, at the University of London, tuition for students of the EU and UK is £9,000, while the tuition for international students is £20,700. Would having the UK citizenship qualify me for the £9,000 tuition?
Also, as a side note, if I get scholarships, loans, and/or grants in the US, would they carry abroad or would I have to apply for them over there?
Thanks in advance 
NO, you pay full pay as a non resident. Tuition rate is based on residency not citizenship, no scholarships or special treatment, Dual citizens are common as muck and Blighty just wants your $$. Look at your target schools for specific info.
http://www.ucl.ac.uk/current-students/money/fees-support/fee_status_proc indicates that, at University College London, to get the lower UK/EU tuition rate, one has to have EU nationality and have resided in the European Economic Area or Switzerland for three years. There are also a few other cases where non-EU nationals with residency can get the lower UK/EU tuition rate.
At the very least, you need to live in the EU even if you’re not a national. A national who lives in the US wouldn’t be considered a EU resident for tuition purpose at UK universities.