1) As long as the number of candidates I'd imagine - potentially hundreds.
2) The Constitution (specifically the Act of Settlement and the Act of Succession) determines the succession. Succession passes through the eldest legimate male line, though Roman Catholics are excluded. The intent of the Act was to make sure the sovereign was always Anglican but I'm not sure if it specifically says anything apart from excluding Catholics. However since the sovereign is also the Head of the Church of England it's pretty much a given that they have to be at least nominally Anglican.
Due to a modification a few years ago after next sovereign primogeniture supersedes sex (i.e. the eldest heir, male or female succeeds, as long as they are not Catholic). I rather suspect that the final legal disabilities against other faiths in the succession will be removed in the near future, provided the monarchy remains around that long.
3) According to the current constitution Charles succeeds. Without a change in the consitution (i.e. a new Act of Parliament) this will not change, though Charles could succeed and then choose to abdicate, in which case the next in line will succeed (i.e. William).