1) I believe that the context of 1 Timothy 2:9-3:7 indicates that men should be in this roll of being Elders in the church context.
2) I believe that this is the only official leadership role that only men should fill.
3) I believe that Elders can gain valuable insight from allowing women, often their wives, to speak into their discussion about shepherding and overseeing the body. While Elders need to retain official responsibility before God for this oversight having women speak into any situation is invaluable.
4) Lydia’s situation (Acts 16:13-15; 4040) is limited because I believe it is circumstantial. It appears that there are no qualified men available to lead when that house church begins. But if Paul is consistent with his own explicit teaching I believe that once there was qualified men they would move into the role of spiritual oversight. There is no mention of who were the overseers here.
5) If there are no men who are unwilling or unable to provide leadership then there seems to be a provision for exceptions where women provide leadership of which Lydia’s situation may be the perfect example of such contingencies at least to start.
6) Passages like Colossians 3:11 are not speaking to role elimination. They are speaking to our equal standing before God as new creations as he speaks to the “new man” (person) in Christ. Seven verses later in verse 18, Paul speaks to “women be subject to your husbands” so it is clear that Paul maintains roles distinctions even in light of our equal standing before God (v. 10-11).
7) This specific leadership role as Elders does not mean that women cannot fill other leadership roles and, in my opinion even teach while men are around. The key issue is that Elders are responsible to protect and uphold the theological faithfulness and biblical purity for the Body. If a woman is teaching anywhere they are under their authority as should any other man or woman be in that local community of faith. This allows women to teach and take public roles and are partners with men in all areas except being an Elder. The Elders can correct anyone under their authority as to theological truth and accuracy.
8) If you see the idea of “pastor” as a gift then women can exercise and engage that gift like anyone else, assuming they have that gift. If you see the idea of “pastor” as a role / position then it is a bit more circumstantial in my mind. The “lead” or “senior” pastor would often be considered in many churches equal to the role of Elders and thus, the better part of practical wisdom to stay consistent with the Word is to not have women as lead pastors even if the title is used for women in other staff roles or positions.
9)Again this all has nothing to do with equality or skill but whom God has chosen to make accountable for a particular role. I know that is very hard to figure out in our culture that struggles with these issues.