What is the ruling on the first and second marriage contracts and the first and second divorces, and is the woman currently with him considered his wife? And if she becomes pregnant by him, is the child considered his son?

The issue of whether a legitimate seclusion (khalwa) between spouses can substitute for consummation (dukhool) is a matter of scholarly disagreement. There is no need for concern as long as the marriage contract has been renewed; your marriage is valid, and the pregnancy and children of your wife from you are beyond doubt. Since you have secluded yourself with your wife, the previous two divorces have taken effect, and only one divorce remains, by which your wife will be irrevocably divorced (bainunah kubra).