Yes, he would be the one standing in line for custody unless he is unfit.
No, the child goes into the care of custodial parents relatives. A motion for emergency change of custody is required. see my profile.
Yes, they do.
If you are the father, the minute that the mother went to jail, you should have gotten custody of your children. If the mother (assuming she is the custodial parent) is incarcerated, then the non-custodial parent should file for an emergency hearing and get custody of the children. State lines are not as important as the welfare of the children.
By applying to a court.
file a child in need of care motion.
If both of the parents have a joint legal custody arrangement, you have to give the noncustodial parent that information. If you have sole custody of the child, you do not have to share that information with the noncustodial parent.
No. Only the court can enter an order of temporary custody. With the non-custodial parent incarcerated and with the consent of the custodial parent the court would likely approve a temporary guardianship that is in the best interest of the child.
Only after demonstrating a pattern of frequent contact
Report that person to Children and Family services and look for legal help to modify your custody agreement and get the non-custodial parent help or in parentingclasses.
No
Custody of the child, or custodial rights to see the child? Either is possible, it just depends on whether you are willing to do the work. see links below
The non-custodial parent can go to court and request custody of the children. A judge will decide which parent should be awarded custody of the children. The circumstances under which the children are currently living, combined with the reason(s) they are not living with you will be a big factor in whether or not you get to keep custody of the children.