Jeez, they still can’t get over that Henry VIII thing? 
Pretty much! 
Right. Need to “confound their papist tricks”.[sup]1[/sup]
[sup]1[/sup] For those who don’t get it, the quoted line used to be in the second stanza to “God Save the Queen”. The word “papist” is now changed to “knavish”, but I prefer the original.
She’s prohibited from being Catholic, but she’s also required to “join in communion” with the CofE. I don’t know how one falls out of communion with the church, though. It doesn’t exactly kick people out for having the wrong beliefs.
In any case, I’m pretty sure the current monarch is much more popular than the church, so it has nothing to gain from picking a fight with her.
The monarch must become in communion with the CoE at the time of ascending the throne; before accession, however, s/he can be Orthodox or Amish or Methodist or Buddhist or whatever. However, being in communion with Rome at any point in your life is disqualifying.
Note that the Succession to the Crown Act 2013 removes the prohibition against being married to a Papist, though, so several members of the royal family who had been barred were restored to the succession after its passage, notably Prince Michael of Kent, who’s somewhere around 42nd in line for the throne, and his nephew the Earl of St. Andrews.
The monarch must be a Protestant - the succession is confined to Sophie, Electress of Hannover "and the Heirs of Her Body, being Protestants ". And, as already pointed out, he or she must be a Protestant who “joins in Communion with the Church of England” - meaning, in practice, that the monarch must be willing to take the sacrament at the hands of an Anglican minister.
The specific ban on Catholics as such related not to the monarch but to the consort. The monarch could marry anyone, of any faith or none, except a Catholic. The ban on being married to a Catholic was removed last year, but the requirement for the monarch to be Protestant, and to join in communion with the C of E, is still in place.
I interpreted it as potentially you could be in communion with the Church of England but also be member of another faith, much like how the first two Georges were Lutherans. I grant it would be more difficult to square with a wholly different religion from Christianity, of course, but in this enlightened age I doubt many would care either way.
I think the law would be changed pretty quickly if anyone wanted it enough, but AFAIK the CofE doesn’t cross-examine its communicants (the whole point of the Elizabethan settlement was that it was about not “making a window into men’s souls”).
I think it’s assumed it’s the RCs who were much more concerned about people taking communion from them as well as from the shop down the road - which is why the ban still remains, since it’s assumed that a conscientious RC could not, in conscience, be in communion with the CofE, and would alsochave to bring up their children as RCs.
Well, you do have to be baptised (in any Christian denomination) to take communion in the Church of England, so any descendant of Sophie of Hanover who was unbaptised would be excluded from the succession.
But if you are baptised in any Protestant tradition, and are willing to take an Anglican Eucharist, you’re good to go. As you point out, George I and George II were both baptised in the Lutheran tradition.
Maybe not. In practical terms, it’s a huge issue to get the Act of Settlement changed, since it requires co-ordinated action between 16 Commonwealth realms, and they all have their own political and legislative priorities. When it was agreed to change the rule that gave male children priority over female children, and that forbid anyone in line to the throne to marry a Catholic, that took four years to implement, and it was pretty uncontroversial. A change to the rule that the monarch must be a Protestant in communion with the Church of England would be controversial, since it calls into question the relationship of the Church of England with the crown and the British state. I really don’t see this as a law that would be changed “pretty quickly” because someone in line to the throne wished to become a Catholic while retaining their place in the line of succession.