As far as i know, you can leave the child with a relative without letting anybody know, but if you leave them in the custody of a babysitter or anything, you must let somebody know, anybody.
Just on vacation should be fine but he would need your permission if the court order can not be fulfilled or if he moves with the child.
interrogation
No
As in taking the child away from the other parent? Perhaps
Arrest
Yes of course you can, theft.
yes.
What does the legal paperwork state? If you are legally bound to request permission from the other, then I would follow that before taking the vacation. Parents who are sharing their time respectively with the child should also provide optional visitation times if the vacation takes any of the visitation that the "other" parent is entitled to.
Only if there is a joint custody order prohibiting the action. If no custody order is in effect, either parent retains the right to take the child or children wherever they choose. This obviously does not include a situation which might place the child in any danger or possibility of such.
You are going to need a lawyer for this. If you do not have funds available, call legal aid. The process involves filing for guardianship through the probate or juvenile court. You'll need to go through a process where you show that you are a fit parent and capable of taking custody. However, it is typically fairly involved, and you will want someone who knows what they are doing to assist.
Read your custody agreement. Everything that governs, or limits, the 'right' of the non-custodial parent during his visitation should be set forth in the custody agreement. If it isn't set forth in the custody agreement then there is no limitation on him. It is, I agree, pretty callous to just take the child off out of state and not give you any contact information. If the custody agreement limits what he can do and where he can go with the child, you could take him back to court asking for the court to find him in contempt of the order, and possibly request further limitations on his visitation.
If the parent with visitation rights has joint legal custody they have the right to participate in the decision to seek and schedule therapy for the child. A parent with sole legal custody has the right to arrange therapy for the child without the consent of the non-custodial parent. The custodial parent should inform the NC parent of the therapy and involve them if the NC parent is willing to help especially when the NC parent is taking a positive parental interest and role in the child's life. However, the parent with sole legal custody has the sole right to make decisions that involve the child. Divorce is often an adversarial situation and judges often do not award joint legal custody if the parents do not have a congenial relationship. That is to avoid a situation where one parent interferes with the needs of the child because they disagree with the custodial parent's decisions.