Typically, if the parties cannot agree to Join Custody the court will have no option but to award sole custody to one party with visitation rights to the other. As a practical matter the presumption is that if the parties cannot agree on the custody arrangements they will likely not be able to agree to day to day decisions regarding the children.
Certainly. You would, however, need to use the "No-Fault" grounds rather than "Separation" if you wanted to proceed with a divorce immediately. The Separation could still be incorporated as a settlement agreement. There is no waiting period required.
As a general rule its always a good idea to have a basic stipulation of settlement in place wherein both parties expressly waive any future claims etc. That said, you certainly can proceed without a stipulation - simply advise the Court in your affidavits that all property has been divided and that neither party is seeking equitable distribution.
A properly drafted stipulation/agreement will ensure that she cannot not make a claim against your assets or future purchases. You may even be able to pursue a divorce and keep her on your insurance depending on several factors. This will need to be discussed with an attorney but is relatively straight forward to accomplish.
It looks like you will need to submit an amended judgment of divorce to the court to be signed by the judge. If your ex is willing to sign off on the amended judgment you can simply submit it to the court along with an affidavit explaining the clerical error.
Generally speaking, if the parties expressly waive rights to equitable distribution of any marital property/assets or debts (including a pension) it is highly unlikely that the Court, on its own, will take issue with such waiver, provided that the agreement was entered into fairly and voluntarily.
If you and your spouse are in agreement these types of issues should be addressed in a stipulation of settlement before continuing with an uncontested divorce. While technically you can attempt to do this on your own, you'd be taking a risk as the court will reject improperly prepared documents - it can also be a very tine-consuming, daunting process for someone with little experience. There are affordable options available for uncontested divorces. Visit www.uncontesteddivorceny.com for more...