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Answer to Question 99.
To understand what Paul is saying we first need to understand that he is not condemning all women who pray without first covering their heads, but only the women of Corinth because this was an important issue in Corinthian society at that time. Historically we know that the female whores of Aphrodite's temple cut their hair very short like the Greek and Roman men. Some even shaved their heads. On the other hand the male whores grew their hair as long as women. If a woman appeared in public without a head covering she was considered as loose and shameless like the whores of Aphrodite's temple.
The head covering was a recognisable sign of obedience and respect to their husbands and also a sign of their own respectability. By removing her covering a woman was automatically placing herself in the category of the ill-famed.
At that time in Corinth, some Christian women, taking advantage of their new freedom they found in Christ, boldly removed their covering during the Church gatherings which scandalized the more straight-laced and prudent. By doing this it was as if they ignored their female gender and their obedience to their husbands which brought shame upon their husbands.
The main reason that concerns Paul is the rank or order of authority between God, the Man Jesus Christ, man and woman and how this order is established during public worship. What he is saying is that there is an order of obedience and respect. Christ is the head of man and man shows his obedience and respect to him and man is the head of a woman and she must show her obedience and respect to him. Thus before a woman begins to pray she must cover her head as a sign of respect to her husband. If she prays without having her head covered she is shaming her (husband).
She might just as well shave her head as the ill-famed women of Corinth.
From this epistle it was assumed that Paul was speaking in general of all women and it became the normal throughout the centuries for women to wear a head covering in Church. In the Russian Church the majority of women still cover their heads in Church, but in the Greek Church this has now became almost obsolete with only a few very old women still covering their heads. Whether there is a right and wrong in wearing a head dress is debatable, but we must keep in mind that Paul was writing to the Corinthians and not to all the Church and also that it was the understanding in their society that an uncovered woman was like a loose woman; this is something we do not consider in our modern societies today. Also the covered head was a sign of obedience and respect to their husbands whereas today those who wear head coverings in Church do so as a sign of respect to God. I personally have no problem with women without head coverings but it is disturbing to see women in Church dressed indecently and with painted faces as though they are ready to go to a nightclub.
To finish with your first question there is no relationship between women's head-coverings and their role in Church. Women do not play an open role in Church services, but they are the backbone of Christian society and without them there would be no philanthropic works. The women's committee of every parish is responsible for organizing events, raising funds and helping those in need. In our parish we also has female choirs, a Greek and an English choir although this also scandalises one or two people because Paul forbids women to talk in Church which is also supported by the 70th Canon of the Quinisext Council. (Does talking include chanting?)
Notice that in the above reading Paul says that men should pray without a head covering yet as your second question notes both clergymen and nuns wear head coverings. Married priests and monks wear a cylindrical hat called a kalymavchi, but with a difference. The married clergy wear a kalymavchi with a protruding rim on top whereas the monastics kalymavchi is without a rim. Married priests should at no time wear their kalymavchion during the services. Outside of Church services the Monks exchange their kalymavchi for a soft cap called a skoufo. Russian nuns also wear a form of the rimless kalymavchi. The kalymavchi symbolises the spiritual helmet mentioned in 1Thessalonians 5:8 (But let us, who are of the day, be sober, putting on the breastplate of faith and love; and for an helmet, the hope of salvation).
During the prayers of becoming a monk the kalymavchi is placed upon his head by the abbot as he says: "Our brother (name) is covered with the kalymavchion of innocence as a helmet and hope of salvation in the name of the Father and the Son and the Holy Spirit, now and forever..." It also symbolises self-denial and devotion to the Divine.
When monks receive the schema they are also covered with the koukoulio or epanokalymavcho. This is a black veil which is attached to the kalymavchi and covers the head the back, shoulders and slightly the breast of the monk. In other words it covers the mind and the heart. It has the same symbolism as the kalymavchi but also that the monk is overshadowed with the grace of God which will protect him and surround his sensual perspectives found in the mind. It also symbolizes the virginal pureness and abstinence of the monks and unmarried clergy (Archimandrites and Bishops).
I don't know what to say about your last question because I did not understand what you actually meant. There is the Sacrament of the Holy Priesthood and also the royal priesthood mentioned in 1 Peter 2:9 "you are a chosen people, a royal priesthood, a holy nation, God's special possession" in which every baptized Christian is a priest. But having said this, the general or royal priesthood cannot replace the Ordained Priesthood. This is something that the Protestants have done. They acknowledge the general priesthood, but they reject the Ordained Priesthood, and this is why they have eliminated the mystery of priesthood.
So even though a woman is a member of the royal priesthood I cannot understand how maternity is a form of priesthood. Also priests do not give birth to souls. The souls are given by God and the priest as a spiritual father has the responsibility to nurture the souls God has entrusted to him with the spiritual food that will help them to spiritually grow in preparation for eternal life. Mothers on the other hand give birth to human beings and as every human is a body and soul entity then with childbirth they do indeed bring forth souls into the world.
With love in Christ