Hi LaGrange, my response is from the perspective of a non-Calvinist.
First, let me illustrate a point. When I was in Junior (Middle) school, I loved to draw "mazes." And as a person would try to draw a line through the many twists and turns, they usually ended up at a dead end, and had to back to find where they had made the wrong turn. And no matter how many turns were made after the first wrong turn, all the rest always ended at a dead end. Reaching the right understanding of biblical doctrine requires we make all the right turns, because once we are off the true path, we end up with false doctrine.
In you first question, you used two biblical terms - soul and sanctification process. The body of Christ, made up of professing believers is split as to what constitutes a "human soul." Many believe humans are made up of three parts, body, soul and spirit. Others (including myself) believe we are made up of two parts - the human physical body and the human spirit/soul.
Thus, according to the turn I have taken, when we are spiritually born anew, our human spirit/soul is altered such that it is a new creation. Then, only after we are spiritually made new, are we indwelt with our Helper, the Holy Spirit.
The second term - sanctification process - appears to by referencing "progressive sanctification" where we grow more Christ-like and a more effective witness for Christ. Here is a verse that addresses the concept:
2Corinthians 3:18
And we all, with unveiled faces reflecting the glory of the Lord, are being transformed into the same image from one degree of glory to another, which is from the Lord, who is the Spirit. (NET)
The key here is to recognize this process, comes after we are born anew, and thus through our love of Christ, are trying to follow Him.
Now let me turn to the many points you made in your last paragraph:
1) Yes, we are caused to be born anew by God alone.
2) Irresistible Grace means something very different in the Calvinist view. In their view it transforms a person unable to trust in Christ, to being compelled to have faith instilled by God. But if you limit your view to just being placed spiritually into Christ, yes that action is irresistible.
3) No, being "dead in our sins and trespasses" does not mean being unable to make holy choices. Many verses demonstrate fallen people can make holy choices, such as the men "entering" the kingdom in Matthew 23:13.
4) Yes we do not "in any way" save ourselves. God chooses those whose faith He, and He alone credits as righteousness, by placing them individually into Christ, where we undergo the washing of regeneration and arise a new creation, born anew by the will of God.
I know you would have to retrace many steps to be able to accept this very different view from yours, but my hope is in God.