Taking your questions one by one:-
1) The Good Old Days of plenty of biomed jobs being available overseas for British biomeds have long gone, unfortunately. But if you're really serious, you might want to join one of the expat organizations (like
this one, for example - although again, biomed jobs are rarely seen these days). You could also try
here.
2) You could try the two
agents well-known to this forum. "Do these types of contracts come up a lot"? I would say:- "yes". But you would need to be flexible about moving around (staying here and there), and (let's be honest) they are not always in the most "sought after" locations or "prestigious" hospitals.

3) In my experience, all sorts of weird and wonderful working arrangements have been (are being) practised. I guess you'll never know until you ask the Boss (the Management, HR or whomever). In short, if they want you (value your contribution) then I reckon it's likely they will seek to accommodate your needs; otherwise ...

Good Luck.
