These two observations generally peek the curiosity of many when they first become acquainted with the Church. The Coptic Orthodox Church is adorned with beautiful and significant symbols and deep meanings. Symbolic gestures represent specific theological messages and spiritual emphasis on key points. Other interested seekers, like you, asked similar questions which we posted on the SUS Diocese website Question & Answer page. I hope these explanations are helpful to you.
RE: The Seating of Women Separate from the Seating of Men
Separation of sexes in the Church was a universal Christian custom until the Protestant Reformation. This often escapes the new generations' knowledge. As a matter of fact, the custom existed among many Protestant churches until the last century...The early church and early church fathers viewed separation of sexes, during religious practices particularly, as an "appreciation of the natural order." It was viewed as a positive occurrence rather than a negative one. Everything had its proper place, at the proper time according to its natural order...In the Apostolic Constitutions, we are told that the Christian faithful were segregated in church not only by sex but many other things as well. These things included age (women, young women with infants, children, and so on) and vocation (monks, virgins, widows, etc)...St. Cyril of Jerusalem points out, the animals entering the Ark, do so with their own kind:
For though the ark was one, and the door was shut, yet had things been suitably arranged. If the church is shut, and you are all inside, yet let there be separation, men with men, women with women: lest the pretext of salvation become an occasion of destruction.
In early Christian writings, the separation of sexes was also seen as a safeguard against temptation. The early Church Fathers did not consider the present-day careless, casual mixing of the sexes to be spiritually healthy.
Further, as early Christianity attests, there were wooden partitions separating the church aisles St. John Chrysostom states:
"It were meet indeed that ye had within you the wall to part you from the women; but since ye are not so minded, our Fathers thought it necessary by these boards to wall you off; since I hear from the elder ones, that of old there were not so much as these partitions; 'For in Christ Jesus there is neither male nor female.' And in the Apostles' time also men and women were together, because the men were men, and the women, women. But it is now altogether the contrary; the women have urged themselves into the manners of courtesans, but the men are in no better state than frantic horses."
St. Hippolytus and the Apostolic Constitutions both specify that the "kiss of peace" is not to be exchanged between men and women. In his Apostolic Traditions, written before 230, St Hippolytus delivered the following instructions for catechumens:
"And let the women stand praying by themselves in another part of the church, whether they be faithful women or women catechumens. But after they finish praying, let them not give the kiss of peace, for their kiss is not yet holy. Let the faithful indeed greet each other, the men with the men and the women with the women; but let the men not greet the women.
As you can easily see that the distinguished custom of separate seating dates back to the early church and has been faithfully practiced by the Coptic Orthodox Church since its conception."
You may also read: http://www.suscopts.org/q&a/index.php?qid=54&catid=76.
RE: Women Wearing Veils During Prayer
Women wear veils to cover their hair during the Divine Liturgy in observance and obedience to the traditions delivered to them: "But I want you to know that the head of every man is Christ, the head of woman is man, and the head of Christ is God. Every man praying and prophesying, having his head covered, dishonors his head. But every woman who prays or prophesies with her head uncovered dishonors her head, for that is one and the same as if her head were shaved. For if a woman is not covered, let her also be shorn. But if it is shameful for a woman to be shorn or shaved, let her be covered. Judge among yourselves. Is it proper for a woman to pray to God with her head uncovered? Does not even nature itself teach you that if a man has long hair, it is a dishonor to him? But if a woman has long hair, it is a glory to her; for her hair is given to her for a covering" (1 Corinthians 11:1-15).
The spiritual meaning behind it is to cover human glory in the presence of God.
You may also read: http://www.suscopts.org/q&a/index.php?qid=1324&catid=626.