1. What does the term Anglican mean? Does it relate to the term Anglo- Saxon in a way? If so please elaborate
2. Just as the Catholic Church has a head church/ top diocese ( the Vatican ), does the Anglican Church have one also?
3. Who is in head of the Anglican Church?
Answer to #3. The head of the Anglican church is the same one who is head of all churches: our Lord Jesus, the son of Joseph, carpenter of Nazareth.
Answer to #2: Anglicanism does not have the bureaucratic centralization of the Roman church. Indeed, this is one of the issues dividing us from the Roman church. The Bishop of Rome's privileges, to us, are mostly man-made, not derived from God. This does not necessarily mean it is wrong for the Pope, as Patriarch of the West, to have these privileges. Only that the Popes' claims about the origins of these privileges are rejected: his privileges are part of the scheme of this world which fades away; they must be modified according to circumstances.
The Archbishops of Canterbury and York are held in very high esteem, and the Archbishop of Canterbury is considered to be a sort of focus or unifying figure for Anglicans. But the head of our church remains Jesus our Lord.
Answer to #1. This is an interesting topic, but there is no simple answer. The English ("Anglo-Saxons") were Germans who were hired as mercenaries by the rulers of southeastern Britain after Britian's defenses were weakened by the departure of the military expedition of A.D. 407. This expedition left Britain with two objectives: (1) to head off a barbarian invasion that threatened Britain, and (2) to enthrone their commander, Constantine, as Emperor Constantine III. They seem to have succeeded in (1), but they certainly failed in (2). In any case, the expeditionary force of A.D. 307 never returned to Britain as an organized fighting force. Hence the states of southeastern Britain hired English mercenaries to bolster their defenses. This worked well until the English rebelled against their employers and set themselves up as rulers of the lands where they had been settled. Tradition carries tales of contract disputes and betrayal, but in any case, English rulers, and the English language, became dominant in Kent, East Anglia, and eastern Northumbria. As time went on, English-speaking rulers came to dominate all of what is now "England": Gloucester (as it is now called) fell to the English in the late 500's, Chester in the early 600's. But the Christian religion of the conquered Britons eventually became the religion of the English, by way of Irish and Italian missionaries, and possibly through the influence of British Christians in some places. (The shrine of St. Alban, for example, seems not to have been suppressed by the pagan English, and was later adopted by the Christian English as their own.) This English church, together with the Welsh and Scottish churches, after passing through many trials and finally rejecting the jurisdiction of the Bishop of Rome in the 16th century, are the original churches of what is now called "Anglicanism". "Anglicanism" developed its own ethos in the 16th-17th centuries, and this form of Christianity spread to the colonies of the British Empire and, from them, to others.
Throughout the world many people are Anglicans who have no genetic connection to he English mercenaries hired by the rulers of Southeastern Britain after the failed expedition of A.D. 407. It is not a matter of ancestry. It is a matter of attitude and theology. The theology at least of "high church" Anglicans can be summarized as "one God, two testaments, three creeds, four councils, five centuries." Anything that was part of Christianity before A.D. 500, if it is not contrary to Scripture, is given at least a provisional pass in Anglican practice, until more careful scrutiny leads to it being fully accepted or rejected. (The popes' claims of supremacy were first made before A.D. 500, but are rejected by Anglicans, at least in the form they now have.)
So you will find some Anglicans for whom the English connection is important. To others, however, this "Anglo-Saxon" heritage might be less important than the Reformation heritage, or the connection to the primitive church of the first five centuries of Christianity. Based on my experience I can state with reasonable confidence that almost all of us will consider Anglicanism to be orthodox Christianity.