Don't be tricked by that sort of talk. It's not uncommon. What they are basically saying is that they would be willing to give communion to an EO person or even to concelebrate, if the other party were willing. They mean something totally different from what you are imagining.
This is also correct. You will actually find a similar situation in some RC churches, though they qualify it with "if your bishop was willing."
Anglo-Catholics, whether they will admit it or not, are the innovators within Anglicanism, which did not exist in any real sense as a distinct body before Edward VI.
Not to entirely derail the thread, but I would say that is incorrect. The tension between Protestantism and Anglo-Catholicism has been around since Cranmer and King Henry VIII. I would also like to point out that Anglo-Catholics, aside from the occasional splinter group (but you'll find that with ultra-low-church as well) do not exist as a separate body in the Anglican Communion, but as a movement within the body.
As regards the Anglican Catholics, however, everything you stated is correct.
I only say this as an interpreter of history, not dogmatically. It is only my opinion.
PerhapsI should clarify: In my readings, the feeling that I got was that through the rule of James II, Catholics in England didn't consider themselves anything but Catholic -- they would not have called themselves Anglo-Catholics, Anglican Catholics, Catholic Anglicans, etc. The prevailing mood of the day would not have allowed for a real Catholic-dissent movement within the church; heck, Charles I (and the Abp. of Canterbury with him) lost his head for being too Arminian. There were certainly Catholic/Anglican tensions in the early years of the Anglican Church's independence, but that is because both hated each other and the Catholics didn't recognize the authority of the Church of England. That is why the last officially adopted prayerbook is still the 1662, which borrowed high-church theatrics but was at its core Protestant. I'm not saying there wasn't a Catholic party in the Church of England, it just didn't consider itself to be an Anglican-Catholic party.
What we identify as Anglo-Catholicism didn't really arise until the nineteenth century, and the reason it didn't tear the church apart then was nationalism. At that time Englishmen basically worshipped the English church settlement, which was as much a part of civic life as the secular government.
Again, this is only my reading of history. The history of the Church of England after 1559 was a very messy affair.