I have been doing a lot of studying on head covering.  At first glance, I felt that a secondary head covering was needed, but I wasn't sure when. Only at worship? During every prayer?  So I got the lexicon out and started combing through the Greek and Hebrew.  I also hit the Internet and read up on various views.  I included one view that seems to make sense to me with the Greek I studied.  But I am still not completely convinced. 

It seems that Paul is talking about a custom of wearing a veil of some sort to symbolize man's authority in verses 3-10. He also makes an implication that men and women are to reflect their sex in dress and hair (men look like men and women look like women). But then he uses the word "However(NAS) or Nevertheless (KJ)" in verse 11- 12 (which is to unfold, expand upon, add more) and says, "in the Lord" we are dependent on each other equally.  Then he seems to come back to the head covering issue and clarifies, stating that : "But if the woman have (Komao- "to let hair grow long") long hair, it is (doxa- "excellence, splendor, majesty") a glory to her; for her (Kome- "hair" (rooted from Komizo- meaning to tend ,to take care of)) hair  is her (peribolaion- "wrapper, veil, mantel") covering." 

1. Is Paul giving a clarification of what the covering is to be in verse 15?  It seems kind of unrelated if it isn't a clarification of the intended veil.  Komao and Kome are used only here.  The other word for hair is thrix - "hair of the head"- like the woman who washed Jesus' feet with her hair (thrix). 

2. Why did he use a special word for hair here if it doesn't have a special meaning?  Also, the peribolaion literally means a garment like veil - also used in Hebrews as a garment Jesus would roll up- from prophesy. I think it refers to the Hebrew word Kacah- a glory cloak, the prophet's garment, and a Maataphoth (tunic worn by women) 

3. I am I right in the translations here ( I am so far from a Greek scholar it's sad)?

Could the chapter be organized like this?   
3-10  Reviewing the Jewish custom of head covering and appropriateness- gender specific roles we have (and appearance)   
11-12 Stating however, in the Lord, we are dependent on each other- equal (although the man does have the leadership authority)[this idea of woman / man relationship is a change from the Old Testament isn't it?]   
13-15 Stating we need to maintain our gender specific appearance and roles - concluding that the long(Komao) taken care of hair(Kome) is to be the woman's covering or veil (peribolaion). 

Am I way off? Like I said, I am by no means a scholar and would greatly value your opinion.  I do pray for wisdom concerning this (and all others) topic.  I don't want to be phariseeical about rules and laws but I do want to please my God!

Yes, there is quite a debate over the meaning and application of these particular verses. I suspect that most originate from the fact that people do not try to understand what was written. Instead they approach the passage to prove what they already believe. Such an approach allows twisting of what is expressed, as Peter forewarned us (II Peter 3:15-16) and leads so useless wrangling about words (II Timothy 2:14-16).

Given the weighty people who have preceded me on this issue, I doubt that I could add anything that would convince a person one way or the other -- especially if they have basically decided what answer they are looking for. However, I can point out where the arguments being made are not proper.

First, let's start with your organization. You start out saying that I Corinthians 11:3-10 is a review of the Jewish custom of head covering. This fails on several accounts

1) Paul states in verse 1, leading into this discussion, that the Corinthians are to be imitators of him as he in turn imitates Christ. The Jews rejected Christ. Thus the discussion is addressed to Christians.

2) Paul states in verse 3 that Christ is head over men and women. Again, this is not what the Jews accepted.

3) Paul uses the present tense for the most part in verses 3-10. He is not discussing what used to be, but what must be.

4) The rules Paul gives do not match known Jewish customs. Jewish men wore a covering during worship. Paul is arguing that Christian males should not wear a covering.

Next, you state that I Corinthians 11:11-12 contrasts to Old Testament teaching that men are leaders, but in the Lord men and women are co-dependant on each other. This idea of a contrast fails because Paul's proof comes from things found in the Old Testament -- the accepted fact that men and women ultimately originate from God (Genesis 2) and that our existence depends on both men and women.

You ask about the word selection in I Corinthians 11:15. The Greek word for "covering" is peribolaion which means a cloak, a mantle, a garment, or some other covering. It is used in Hebrews 1:12 to refer to an outer garment that has worn out. It was used by the Septuagint translators to refer to a garment, a cloak or covering, clothing, an awning, raiment, or a veil. In the most literal sense, the Greek word refers to something that is put on. The Greek word for "long hair" is komao and the word for "hair" is kome. The word kome is used exclusively for human hair when the appearance of that hair is being emphasized. I suspect that kome was particularly used because it goes well with komao. The related Greek word, thrix, refers to any physical hair, human or animal. It is not used at all in I Corinthians 11. Arguing about why God, through Paul, selected kome over thrix is really a none issue.

The use of "nevertheless" or "however" at the start of I Corinthians 11:11 is a fairly common method used by Paul to qualify what he is saying so that people don't go overboard in applying his discussion. He has made several arguments that man is over the woman, but he doesn't want people to walk away thinking that men are better than women. While men have been assigned the role of leader by God, in the Lord, that is in the church (I Corinthians 4:17; 7:22; 9:1; 15:58; 16:19), men and women are equal. This is the same as what Paul told the Galatians, "There is neither Jew nor Greek, there is neither slave nor free, there is neither male nor female; for you are all one in Christ Jesus" (Galatians 3:28). See Ephesians 5:33; Philippians 1:18; 3:16; 4:14 for other examples of "nevertheless" as used by Paul.

That a woman's long hair is the covering considered in I Corinthians 11:5-6 does not make sense because a woman is to have the covering when she is praying or prophesying. This implies that it is only needed for certain occasions. But a woman's hair is not something you can take on and off as the occasion demands. Therefore, Paul is not saying that a woman's hair is that covering. Instead, he is arguing that having to put a covering on is not a great burden because a woman is already used to her natural covering. Just as the rule for a man not to cover his head is not "unusual" or "unnatural" because men are already used to wearing short hair.

See also:

Questions and Answers regarding Head Coverings