Response to Vital Questions
1. What happened in the Garden?
This question I think addresses the issue of how was natural mans nature
altered supernaturally by God's curse? Clearly they were separated spiritually from God. They were expelled and precluded from re-entering. And as a result, all mankind is conceived in inquiry, in a spiritually separated from God state. When scripture says we were "made" sinners, for sure it means we are spiritually "dead" meaning separated from God as unable to do anything to re-enter the "kingdom of God." But it gets worse. Recall when Adam sinned, both Adam and Eve's eyes were opened? This speaks to their spiritual corruption, resulting in mankind's predisposition to sin once we know right from wrong.
I think most of us would agree with the above. Where we part ways is the assertion that being spiritually dead, separated from God, result in total spiritual inability, unable to respond to the gospel. I believe fallen natural man can understand the milk of the gospel, such that we can trust in Christ in a way which God could choose to credit as righteousness, Romans 4:5.
2. What happened at the Cross?
Here the question probably addresses whether Christ died for the supposedly preselected elect, or whether Christ died as a ransom for all. Since false teachers have been "bought" I think Christ died not only for us but also for the whole world - referring to all mankind. But reconciling the world does not mean anyone received that reconciliation. Only when God credits our faith as righteousness and spiritually places us in Christ (the sanctification by the Spirit) do we receive the reconciliation, and become one of the redeemed.
I think the illustration of the oil lease best illustrates what was accomplished on the cross. Picture a "Big Oil Man" buying a lease for oil on a section of ground. He now has the right to extract all or some or none of the oil, but the oil so to speak has been bought with a price. Now when He extracts some oil, it is like God transferring us from the realm of darkness into His kingdom. Similarly all mankind has been "bought" but only those whose faith God credits as righteousness and spiritually placed "in Christ" receive the reconciliation.
3. How is it that a sinner believes on Christ?
First the sinner must hear the gospel, and then have sufficient spiritual ability to respond appropriately such that God credits their faith as righteousness. It is possible to hear such a corrupted gospel (another gospel) that misses the mark so far as to not provide the opportunity to respond appropriately. I think this happened in Matthew 23:13.
Second the sinner may have hardened his or her own heart such that it is as if they never heard the gospel, what limited spiritual ability they had has been lost, like the first soil of Matthew 13. (And of course, in Romans 11, we see that God has hardened the hearts of some, for His purpose, such that they could not respond, in order to spread the gospel.)