Legal Custody

EX wife is asking for my 50% legal custody and I am considering giving it to her, but before I do I need some questions answered and I hope I can get them here from all the wonderful people that help answer on the forum.

Ok here it goes,

On the court forms there is sections that can be checked. Can it be made to give her full legal custody of our 2 kids with the following stipulations :
She cannot move the kids out of state, I can make medical decisions on the health, she cannot change their last name and the school can contact me in case of emergency first before calling others. So is possible that the court can say ok EX WIFE you have full custody of the kids but with these stipulations. Can that be done and if so will it hurt me legally in the long run ?

I currently pay $ 600 a month for 2 kids, is that alot or should I be paying more. The $600 is what we agreed on at court at the divorce 4 years ago and she is willing to leave it at $600 and I can make the schedule for my visitaions and Holidays ...

Also can someone tell me the difference between Legal Custody and Parental rights ?

Thanks for all the advise

You can agree anything you wish--legal custody means you make the major decisions and have control over most major issues.