1. If your husband WANTS primary custody of his son, he should take her back to court with a motion to modify the order of custody. The sooner he does so, the better his chances of getting custody since his son has been with him (you) for the past 5 years. That weighs in your favor. It is not likely a court would grant retroactive support as your husband had the right to file a motion to modify the order when his son first started to live with you, but they could terminate any order in place if he is granted primary custody.
2. No. The mother cannot take the things you and your husband have purchased for him. They remain in your home for when he is with you.
3. He could get a restraining order against her (it's possible), but it may be better to use such evidence to gain custody rather than a restraining order.
4. No. When one files for a restraining order, the court may grant a temporary one, but a hearing is required to make it permanent. Otherwise, it expires in 10 days or so, depending on the jurisdiction you are in.
Please let me know if you need additional information.
Best regards to you,
TG
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She could try, but the court is unlikely to order payment if it is clear that he was living with you.
All the best to you and your family.
Lawyer.
licensed attorney for 12 years including employment, business, contract, domestic, and general civil