Ok, so far so good.
So the ecclesiastical independence severed the hierarchical order as well? Say a Bishop in New York is not longer overseen by other Bishopric Office in England?
Yep. The American Church is independent.
Does the Queen participate in the General Synod?
And can Her Majesty exercise authority in matters of Faith and Morals?
In practice, not really. She opens Synod, much like she opens parliament; likewise the two are seen as receiving legislative authority from her.
Does it work in like manner to the Orthodox? Several Independent Bishopric Offices in agreement with one Faith?
In theory, though not in practice!
Would you mind listing the different Anglican Churches? Sorry if they are too many
From wikipedia:
All 38 provinces of the Anglican Communion are autonomous, each with its own primate and governing structure. These provinces may take the form of national churches (such as in Canada, Uganda, or Japan) or a collection of nations (such as the West Indies, Central Africa, or Southeast Asia). They are, in alphabetical order:
Anglican Church in Aotearoa, New Zealand and Polynesia
Anglican Church of Australia
Church of Bangladesh
Igreja Episcopal Anglicana do Brasil (Anglican Episcopal Church of Brazil)
Anglican Church of Burundi
Anglican Church of Canada
Church of the Province of Central Africa
Iglesia Anglicana de la Region Central America (Anglican Church in the Central Region of America)
Province de lâĂglise anglicane du Congo (Province of the Anglican Church of Congo)
Church of England
Hong Kong Sheng Kung Hui (Hong Kong Anglican Church (Episcopal))
Church of the Province of the Indian Ocean
Church of Ireland
Nippon Sei Ko Kai (Japan)
Episcopal Church in Jerusalem and the Middle East
Anglican Church of Kenya
Anglican Church of Korea
Church of the Province of Melanesia
Anglican Church of Mexico
Church of the Province of Myanmar
Church of Nigeria
Church of North India
Church of Pakistan
Anglican Church of Papua New Guinea
Episcopal Church in the Philippines
Church of the Province of Rwanda
Scottish Episcopal Church
Church of the Province of South East Asia
Church of South India
Anglican Church of Southern Africa
Anglican Church of the Southern Cone of America
Episcopal Church of the Sudan
Anglican Church of Tanzania
Church of Uganda
Episcopal Church of the United States of America
Church in Wales
Church of the Province of West Africa
Church in the Province of the West Indies
In addition, there are six extraprovincial churches, five of which are under the metropolitical authority of the Archbishop of Canterbury.
Anglican Church of Bermuda (extraprovincial to the Archbishop of Canterbury)
Iglesia Episcopal de Cuba (Episcopal Church of Cuba) (under a metropolitan council)
Parish of the Falkland Islands (extraprovincial to the Archbishop of Canterbury)
Lusitanian Catholic Apostolic Evangelical Church (extraprovincial to the Archbishop of Canterbury)
Spanish Reformed Episcopal Church (extraprovincial to the Archbishop of Canterbury)
Church of Ceylon (extraprovincial to the Archbishop of Canterbury)
In addition to other member churches, the churches of the Anglican Communion are in full communion with the Old Catholic churches of the Union of Utrecht and the Scandinavian Lutheran churches of the Porvoo Communion in Europe, the India-based Malankara Mar Thoma Syrian and Malabar Independent Syrian churches and the Philippine Independent Church, also known as the Aglipayan Church.