Your consent for the annulment process is not needed. Your particpation in an annulment process is not required. All that is required is that the Tribunal make legitimate attempt(s) to make you aware that the annulment has been requested and advise you of its outcome. If your ex-husband did not have current information on your location, or you chose to ignore any contact from the Tribunal, it is certainly possible for the process to have taken place without your knowledge. Not probably, but possible . . .
no not entirely true
every effort must be made to locate both parties and for them to submit their own intervew, witnesses etc., the same due diligence in locating witnesses as would be exercised in any legal proceeding. Only if you failed or refused to respond could the tribunal proceed without your (name removed by moderator)ut. You apparently are on top of things, and if you feel your marriage was in fact invalid, may want to initiate proceedings yourself, precisely to make sure your side of the story is heard, and of course, so that if this proves to be the case, you are free to marry.
If he was indeed Catholic, and married you and wife #2 outside the Church, without regard to her marriage laws, neither of his first two marriages was valid, and he can prove that by presenting the necessary paperwork, without a formal annulment investigation.
As I said, there are simply to many factors to give an answer here, baptismal status of all parties involved, previous marriages of all parties involved etc. At the very least the priest preparing this unfortunate girl for marriage is obligated to make sure this man is capable of entering into a valid marriage and has proper intent, and would be quite justified in delaying the marriage until such evidence is presented, or refusing to marry them.
the status of your children is not affected. Illegitamacy is a legal, not church issue, and no state uses that term anymore, I think. If they have been baptized Catholic they are Catholic, and are bound by Catholic law, in marriage, sacraments and other issues, so deserve to be brought up and educated in that faith, so they understand those obligations.