Who is "she"?
To answer your first question, the "she" in verse 15 probably refers back to the she in verse 12 ("she must be silent"). For "she" to refer to Eve would seem like a digression. It's better to think Paul stays on point.
What does it mean for her to be "saved through child bearing?"
Having read numerous attempts at a reasonable interpretation, I've found Andreas Köstenberger's exegesis the most convincing. The article is for the CBMW, and anyway the issue is emotionally charged, so it's important to me that his arguments stick close to the text. And indeed, he surveys a number of texts; here are three key ones:
1 Timothy 4:16 - Watch your life and doctrine closely. Persevere in them, because if you do, you will save both yourself and your hearers.
1 Timothy 5:14-15 - So I counsel younger widows to marry, to have children, to manage their homes and to give the enemy no opportunity for slander. Some have in fact already turned away to follow Satan.
1 Corinthians 7:5 - Do not deprive each other except by mutual consent and for a time, so that you may devote yourselves to prayer. Then come together again so that Satan will not tempt you because of your lack of self-control.
First, as you remark, a natural reading of the word "saved" doesn't allow this passage to agree with the rest of Scriptures. So we should look at possible defintions. One possibility comes from 1 Timothy 4:16 above. It's plain from that verse that Paul does not think that in the final judgment Timothy's listeners will be saved on the basis of Timothy's careful watch of his own life and doctrine. Rather the idea is probably better seen in a place like 6:20-21: "Timothy, guard what has been entrusted to your care. Turn away from godless chatter and the opposing ideas of what is falsely called knowledge, which some have professed and in so doing have wandered from the faith." Therefore, we might understand "save" as in the sense of "protect someone from wandering from the faith."
Second, then, we ask how does "childbearing" protect anyone from wandering from their faith? The phrase "to have children" in 1 Timothy 5:14 is the only other instance of this term in the New Testament. And here we see it alongside a couple other verbs: "marry" and "manage their homes." It's possible then that Paul's use of childbearing in 2:15 is a shorthand for this larger idea. In the passage in chapter 5, the young widows are in danger of bringing judgment on themselves by being idlers and gossips and busybodies. To protect them from this, Paul counsels that they marry, have children, and manage homes. This will keep Satan from getting a foothold in their lives.
We see a similar pattern in the 1 Corithians 7 passage. Paul is concerned that by depriving one another couples will give opportunity to Satan to tempt them towards sexual immorality. Paul therefore recommends that they come together as a married couple as a means of protection. Thus while we wouldn't say anyone is saved in the final judgment because they had regular intercourse with their spouse, people might be saved from the temptation to go after shrine prostitutes and their idols and so forsake the faith.
Similarly, childbearing is not what saves a woman in the final judgement. A woman is saved in the final judgment like anyone else (their is no Jew nor Gentile, neither slave nor free, nor is there male or female...): through faith. Yet in this life, childbearing is a gift to help save her from making shipwreck of that faith.
There is a problem with the English translations of this verse.
In the kJV it reads "they shall be saved in childbearing". The ASV says "saved through her child-bearing". The CEV says "will be saved by having children". And, the ERV says "will be saved in their work of having children".
Does anyone stop to think that these translations set up a different method of salvation for women than for men? Women then would not be saved through baptism into Christ (Acts 2:38; Mark 16:16), but through works of bearing children?
What about those women who are barren and cannot have children? Or, what about those women who never marry? They cannot be saved?
These questions should let us know that the translation is incorrect. Young's has translated it correctly.
"and she shall be saved through the child-bearing, if they remain in faith, and love, and sanctification, with sobriety." (YLT)
Is it not more clear? Which child-bearing? Hers, or "the"? It is confirmed in the Greek Interlinear transliterated as "dia tes teknogonias".
John 3:5-6.
"Jesus answered, Verily, verily I say unto thee, except that a man be born of water and of the Spirit, he cannot enter into the kingdom of God.
6 That which is born of the flesh, is [i]flesh: and that that is born of the Spirit, is spirit."
7 Marvel not that I said to thee, Ye must be born again." (GNV)
THE child-bearing is not of the flesh, but of the spirit. We all must be born again of the water and the spirit through baptism into Christ.
The verse is not speaking of a woman's act of child birth. That would make salvation of works. A woman is saved the same way a man is saved - through the birth of the water and the spirit.
"Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new." (2 Cor. 5:17, KJV)
"And that ye put on the new man, which after God is created in righteousness and true holiness." (Eph. 4:24, KJV)
"And have put on the new man, which is renewed in knowledge after the image of him that created him:" (Eph. 3:10, KJV)
There is a lot of delivery and birth language in the NT which is all symbolic of the birth of the church of Christ, and the birth of the new spirit of man in Christ. God does not separate women out from that salvation plan. Both men and women are co-heirs of the promise (Rom. 8:17; 1 Pet. 3:7).
