Two First Sins?

As I understand Genesis 3:17, Adam sinned only by eating from the forbidden fruit. "Listening to Eve" or "obeying Eve" was another (and redundant) way of saying "eating the fruit." We have no record of Adam having been commanded not to listen to Eve, and understanding these statements as synonymous agrees well with typical Hebrew literary patterns.

Also, the traditional idea that Eve sinned by saying "or touch it" doesn't sit well with me because Moses called no attention to this statement in the curse/judgment of Genesis 3:14-19. If this had been a sin, it seems to me that God would have said something about it later, and/or that the serpent would have picked up on it and used it to his advantage. Also, we really have no way of knowing that God did not say this. The account we have is certainly greatly abbreviated, and God may have actually said these words when he gave the initial command, and/or he may have said them later. One might also argue that Adam added the words -- Eve was not around when the command was originally given (Gen. 2:16ff.). In any case, I'm hesitant to call it a sin since the Bible neither calls it a sin nor indicates that Adam or Eve was punished for the addition of these words.

I'm a little unclear on what idol may have been set up in the garden...

Regarding your specific questions:

1. I think Eve sinned before she ate the fruit only by deciding she was going to eat the fruit. I don't think her wording was sinful, and I don't see any evidence of idolatry per se in the passage.
   
   
2. I don't think Adam was with Eve and the Serpent. If he had been, God certainly would have judged him for letting his wife be so misled. As the story reads, it appears that Adam first learns of the situation from Eve, not from observing the dialogue between Eve and the Serpent. Also, Adam's character is not introduced in this scene until after Eve eats, indicating that he was not previously present. Since I don't see any evidence of idolatry, it also does not seem to me that he sinned by failing to oppose idolatry.
   
   
3. It appears to me that Scripture testifies to a single sin of Adam that infects us, not to a dual sin (Rom. 5:12-19 seems to speak consistently of a singular sin).
   
   
4. Insofar as Paul referred to Genesis 2-3 to deny women the right to teach and hold authority over men (1 Tim. 2:11-14), I think it is quite legitimate to look to Genesis 2-3 in the current debates. The fact that Paul appealed to creation indicates to me that the case against women in authoritative roles has permanent validity, and was not simply a cultural stipulation. However, I do not think that Paul was making the case that a woman may never teach a man anything, or even that she may never teach a man theology -- in Acts 18:26 Luke wrote favorably of Priscilla's involvement in Apollos' instruction. Rather, I think the fact that Paul immediately went on to speak about the qualifications for the office of elder (1 Tim. 3) indicates that his statements in 1 Timothy 2:11-14 referred to women holding ruling/teaching offices in the church. As further support of this, he cannot have meant that women were never to speak in church (1 Tim. 2:11), because in 1 Corinthians 11:5 he expected women to be praying and prophesying in church. He did not tell them to stop, but only to wear proper head coverings when they did so.
   
   
5. I think it is reasonable to suggest that because Adam is our federal head and not Eve, we ought to have male authoritative officers and not female. The typology of the creation reasonably implies male primacy in this regard, which I think was Paul's point in 1 Timothy 2:11-14. The fact that Eve sinned first doesn't strike me as terribly significant in this regard -- Paul seems to have been far more interested in her being deceived (implying that Adam was not deceived, and sinned with greater rebellion) than in the fact that she sinned first. And in my understanding, he uses her deception to argue against women ruling, not against them teaching/preaching in general. It doesn't seem to me that the creation ordinances or Paul's use of them justify barring all women from filling preaching/teaching roles in church. In this respect, I think it is better to treat them as unordained men, allowing them to fill a pulpit, but not to rule.