My DD is in Upper Sixth, and has offers from both UK and US universities to start this autumn.
If your DS does apply to the US, he needs to be aware that he will in all probability have to do SAT exams (these are the same exams the US students do, but you can sit them in this country) - we only found one that didn't require this or the alternative to SAT (which I can't remember the name of!).
You can apply to as many universities as you want, but pay for each application. There is one common application form, a bit like a UCAS form, then each university can ask several questions of their own, so if you are applying to lots of different institutions it can be quite time consuming!
Would also say that the US approach seems to me to be more "holistic" than the UK one, and they will genuinely be interested if someone has Grade 8 clarinet, represents the school at hockey etc.
The Fulbright Commission is a good place to look for initial information. They also hold an event in the autumn at which various universities are available to answer questions, and there are a couple of lectures about how to apply, and how to finance it. We went to one at Kensington Town Hall, but I think they take place in other cities too. Kensington Town Hall was way too small, and it was well nigh impossible to speak to any of the universities, although we did get some brochures. The talks were very useful. I have a feeling that the London event has now been moved to somewhere with higher capacity!