1) Judge may only care if you show harm as a result. Otherwise, not seeing it go anywhere.
2) GAL's usually don't care about finances, although notification of appointments may be a factor to look at. Read the 602 statute, look at the factors the court considers - think smarter, not harder. Also, don't don't don't (tattoo this if needed on arm) even think about crossing swords with the GAL. Nothing turns a 10k case into a 50k case faster than a client who crosses swords with a GAL.
Talk to a family law attorney in your area for specific guidance.
You don't need a judge's order to insure your kids. You do, however, need your ex's cooperation or a court order to claim them on your taxes.
She might get in some trouble if HFS finds out. To find out what might happen, you should call HFS and ask them rather than fish around in an online forum.