Paychecks in themselves are not "property." The money derived from the paychecks, to the degree they're deposited into an account, become an asset in that way. It's the assets themselves which need to be addressed in the pre-nup.
The short answer is that military law in inapplicable in this instance. That said, the biological father must be found to have "legally abandoned" the child, meaning lack of substantial contact in the 6 months preceding the filing of the petition. It appears you would have a good case. For a full assessment, schedule a consultation with a NYC Family Law attorney.
This question is too broad to answer as posed, because any document could conceivably be entered into evidence. Generally, documents are "hearsay," but there are many exceptions. For example, certified business or government records could go into evidence. Statements of a party recorded in a document (like an e-mail or text) could go into evidence as either an admission or prior inconsistent statement. Other documents could be the subject of a Notice to Admit and/or fall under another...
I know for a fact there are lawyers in Westchester who offer free consults & sliding scales on their fees - you just need to keep shopping around (try the "Find a Lawyer" tab on this site). Many lawyers don't necessarily advertise that they offer free consults & sliding scales simply because they may reserve them for financial needy clients (i.e., discounts may not be open to everyone).
One can request joint counseling and/or mediation, but it cannot be imposed on the other party by the Court. Moreover, there are many other claims one can make beyond division of assets - what claims you may have should be the subject of a full assessment by an attorney. Thus, you should call a NYC Divorce attorney to schedule a consult.
There's no need to attach the stipulation of settlement to the summons upon filing. Indeed, you can't, simply because the stipulation is a separate document & you must pay a court fee upon it's filing. Theus, you're much better off just resolving the case, have the stipulation signed by both parties & thereafter filing it along with the judgment package. Schedule a consult with a NYC Divorce attorney for more info.
Generally speaking you are not entitled to the other spouse's inheritance. And it is true that issues not raised at the trial level , generally-speaking, cannot be raised for the first time on appeal. For a full assessment, schedule a consultation with a Westchester Divorce attorney.
The press probably filed a motion with the court (which was at least partially granted) or had the parties' consent. You would need 1 of those 2 things in order to gain access to Family Court records, as they are all presumptively confidential, even on celebrity cases.
Generally you're right on the border (in terms of age of child) where the court considers his preference to be a very strong factor. It means by the time you'd hit a trial, he'll be 14 & his preference will likely carry the day. For a full assessment, speak to a NYC Family Law attorney.