Hardly a weird question as you WILL be moving to a different country and they're all different. In my experience anyone who thinks their question is silly is almost always wrong!
Actually you would not be technically adult. You become legally adult at 18, but there are some things that are possible at 16. You commented on passports - that's another matter: if you are British you have to apply for your own passport at 16 instead of having a parent sign the form for you, and the passport will last 10 years instead of 5 as it does for a child.
But the key age is 18. Under 18 you can't buy alcohol or tobacco, you can't vote, you can't enter into a legal contract (to think of a question that often gets asked on this site, that makes it difficult to go away by yourself if you're under 18 because it will be very hard to find a hotel that will accept your booking), and as Guru Hank says you can get married at 16 or 17 but only if your parents consent.
A slight oddity is that 17 is the legal age to drive a car. I have no idea why that's different from everything else! The British driving test is a STIFF one and on average, people pass second time. I did. My former church once had an American minister and she said that what we thought of as a wide road in a town was only small to her. So it needs to be a stiff test as you need to drive more carefully. That's a more general point too - things might seem small to you, including houses.
Alcohol has a slight tweak to it. It is legal for 16 year olds in England to drink in public IF someone over 18 bought the drink, it is beer, wine or cider, AND it is to go with a sit-down meal. So let's say you all go out to a pub or restaurant and your parents want to buy a bottle of wine to go with the meal. If you're over 16, you can have some too. (When I was your age this was possible at 14... it was the last Labour government that put the age up.)
It IS a different culture - don't let the fact that we speak English fool you! We're much more like the rest of Europe than the US. The language is different and to start with you might have trouble with that. For example, we don't have sidewalks in England, we have pavements! You'll pick it up, and we get so much American TV that people will understand. Just be polite and be ready to learn and you will be fine.
I must mention education. The main exams we have are GCSEs at 16. After that, you can leave and get a job as long as it includes training until you're 18, or you stay at school or go to a further education college to study for A levels (you need these to get into university) or some other qualifications. So you are at an awkward age to fit in with that, especially as I understand that because of how American schools work, you probably won't have sat any public exams because you go for your high school diploma at 18 (feel free to correct me!) Never mind, your parents and the local council will sort out what you can do and how you can get some qualifications.
A levels involve a lot of narrowing down as you only pick 3 or 4 subjects to do. So you get to a high standard in those but drop everything else. To take me as an example, I was good at school and what I was most interested in was science, especially physics. So when I was 16, I had to make my A level choices and I did maths, physics and chemistry. That's all I studied for 2 years, and that was quite enough as each subject had a lot of content. It makes British university courses shorter because we start from a higher level - certainly Americans can forget about getting into one unless they've done some subjects at AP, which is about equivalent to A level.
Were you born in the US? If yes, you are a US citizen and US law requires that you enter or leave the US on your US passport. So you'll need one of those to get here, even if you are also British by descent from Dad and have a British passport as well. If you've got both passports, you show the US one when you leave, and the British one when you enter Britain. That gets you through much quicker this end as you can join the EU queue with Dad :)
There's another point... do you know what the European Union is? The UK is a member and any citizen of an EU country can live and work in any other. Just move, show your passport from another EU country, and you're in. So at the airport, it isn't a "British only" queue, it's an "EU only" queue.
For just one last parting shot, remember we drive on the LEFT. So when you're crossing the road, remember that where cars are coming from is in reverse.
Sorry, but you are considered an adult at 18. You can't even drive until you are 17. You can get married at 16, that is the 'age of consent'.
You will actually find that there are fewer differences between America and the UK than you would imagine. All cities seem to be turning into the same city in a lot of countries.
No, you are not an adult at 16, it's 18 in the UK.
How are you are your parents moving to the UK? What visas do you have?
Read Kate Fox's "Watching the English"