It is possible, however it depends on the circumstances. There would have to be a full investigation, followed by an order of the court. It is not an easy thing to do, unless the circumstances are extreme, at least in most cases.
If you live in the US... Unless Mom's parental rights (different thing than custodial rights) have been terminated or she can be proven unfit, she's first in line for custody, so if she wants custody, she will get it (no matter what Dad wants)
Well if the noncustodial parent wishes to take the kid the judge might give the parent custody if there is not a bad reason the parent did not get custody in the first place hope I helped you
That's up to the judge. see link
Preparesee links
If you live in the US... Children are not property and therefore cannot be 'willed'. You can state in your will who you would like to receive custody, but the court is not required to abide by it. For example, if Mom has custody of a child, she dies and her will states that she wants her sister to receive custody, but Dad wants custody...Dad gets custody, unless he can be proved unfit, because Dad has first legal right to custody (Mom's wishes don't change that).
Either parent can have physical custody in a joint custody arrangement. If there is a court order granting the mother physical custody the father should notify the court of the mother's incarceration and have that order modified unless he wants the mother to resume physical custody when she is released.
see links below
If the son wants to I believe he can. In my state (Georgia) the child can choose who he/she wants to live with at the age of 14.
Generally, custody orders end at age eighteen and the child can choose where she wants to live.
This seems extremely unlikely.
Father must petition for custody and court will weigh what situation is best for the child
You must return to court to petition for a modification of the custody order. You should seek the advice of an attorney who specializes in custody issues.