What are the chances of PhD studentships for medical students who are doing their intercalated BSc (Hons)and decided to do a PhD before the clinical years? Are their chances the same as biology students who are doing the same BSc (Hons) subject.

Although we have never heard of anybody doing this, it is likely that it is possible. However doing a PhD as a fully qualified medical doctor is usually much better paid and to be frank much easier (as you will probably get access to technical assistance) than doing a PhD any other way (except buying one of those dodgy ones of the internet).

I would like to ask if medical doctors doing PhD are paid as much as they would be if they work for the NHS? How about those from non EU countries?

As I understand (from my medical colleagues) the usual research training route for doctors is to do an MD (medical doctorate, which takes 2-3 years) when they have reached registrar status i.e. have been qualified doctors for several years. As they usually continue to have NHS clinical responsibilities, I think their salary remains much the same. There is often an option for to transfer from MD to PhD (in a similar process to the Mphil/PhD transfer).

How about medical graduates doing PhD straight after graduation? Do they get paid like working for the NHS?

I wouldn't have thought so, never heard of this situation. Straight after graduation is the pre-registration house officer year, I wouldn't have thought this was an ideal time for a PhD, unless a person had decided that medicine wasn't the career for them and instead wanted to pursue a research career.