They can't debate with other men, nor try to show their husbands, from the scriptures, that they might be going into a false belief.
Women are submissive to husbands, I think that's what the OT is meaning and that's the order God designed. This does not mean they are least, they are equals.
A football team comes to mind. All are equals, but when it comes to the decisions, the QB makes the calls.
I think women are to be submissive UNTIL her husband is acting not according to Scripture. I think she's got every right to speak against it, they are not excluded from the rest of Paul's writings. However when it comes down to two personal opinions perhaps not rooted in solid scripture (IE, it's silent on the issue), I think that's when the man takes precedence and the woman needs to submit and follow.
Because of this as well, is when the commands for them not to be elders or anyone in spiritual authority in the church.
The hair passage is also describing authority. Women identify themselves with long hair. It's submission to the headship because her hair is longer than her husbands, it distinguishes them.
This is a sticky one. Culturally, this was applicable to their culture. In America, we don't identify hair length as any time of authority, so it does not have the same meaning as what it did in Paul's day, and thus we've stopped doing it.
Culture in Biblical context is a sticky situation indeed. It's just like coveting your neighbor's donkey... Do we limit that to their culture of the day? Or do we take the idea and apply it to our culture? I think the latter is what we do.