Normally they ask you to sign an extension voluntarily. If you don't, you will go back in front of the judge he will get to decide if it is extended (and yes, if you made a good faith effort they are not supposed to do so). So don't sign, get an attorney to represent you at the hearing and try to fight it!
unless there is a prenuptial agreement, all property is considered marital under the statute; however, most courts in Winnebago County will allow it to be excluded but the burden is on the one that wants it excluded to convince the judge (or the other side if an agreement is reached) that it is appropriate.
Most of the time any recordings are not admissible in court (though it is permissible for you to record any conversation you participate in); however, while not admissible if a GAL (guardian ad litem) is appointed by the court to give a recommendation as to what they think is in the kids best interest, the GAL may listen to the recordings.
File a motion for contempt on the divorce issues. You can get copies of her tax information to verify her income and ask for sanctions.
As for the identity theft after divorce, call the police and report it. They will investigate and likely charge her with a crime.
don't be penny wise and pound foolish, at a minimum have an attorney look at it before you sign it. Spending some money now could save you a ton of money later when you have a good agreement that deals with the contingencies you need. It is always more expensive to fix errors later than to do it right the first time.