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It is most surely worth your while to hire a family lawyer. Her lawyer is fighting for her and you don't even know what the lawyer said if she is repeating it. It is quite likely that you will be able to resume shared custody because the child is older and it won't be a major change and because you had shared custody until recently.
I don't think you should be so afraid of losing simply because your ex-spouse or her lawyer says you will.
The best way to proceed, without a doubt, is to see your own lawyer.
Any agreement about child support is not binding. She can end up getting her way and then she will come after you for child support.
As well, there's no possibility that you have to pay for all of the private school if your son ends up going to private school as you both have to contribute to this type of expense in proportion to your respective incomes.
Please do not consider agreeing to anything without getting independent legal advice from your lawyer.