Hi Sleepy.
1) Busiest area in the UK is anywhere in the South East, especially around London.
2) You can not fly a single-engine aircraft into Heathrow. As far as I'm aware there is nothing stopping you flying a light twin there, except for extremely high landing fees. I believe there are schools at places like Luton and Manchester, although I'm not 100% sure
3) Not really sure I understand what you're looking for with regards to your final question. There are quite a few differences, and they are quite diverse, so can't really summarise them in just a few sentences. I would guess the three biggest differences would be first of all differences in uncontrolled fields (air/ground radio or AFISO in the UK, Unicom/multicom in the US), secondly the fact that open airspace is generally class G in the UK and class E in the US (big difference for IFR flight, not much difference for VFR), and thirdly the generally poor attitude towards GA, which can be seen in things like landing fees (especially at large airports), ridiculous noise-abatement procedures, lack of radar cover in very busy airspace, and other areas.
Hope that helps,
FFF
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