Yes.
Yes, she can. If the father doesn't like it, he can petition the court to modify the custody agreement.
No. The courts are not yet taking physical control over the bodies of women.
The federal Violence Against Women Act requires it.
yes, she can get a divorce in a Canadian Court however, the custody of said child will have to be a decision for a family court judge
This is interpretive. Generally under the Uniform Child Custody Jurisdiction And Enforcement Act ("UCCJEA") they are suppose to, however this does not preclude other conditions. A mother can run to another state than claim a fear of domestic violence. This than invalidates any orders from another state under the Violence Against Women Act. Unfortunately, the states also have a history of not honoring father custody orders from other states or countries. The was a case of this in Clay County, Missouri. The father with an order from Texas had to kidnap his child and return the Texas.
If there is a court order for custody, visitation or child support she will need his permission. See related question link.
Section 21 of Protection of Women from Domestic Violence Act 2005
Not necessarily, but be advised that there is an interstate compact in effect among all states that they will each enforce the findings of the others child custody orders. Maryland may assist in the return of the child if the Indiana parent has legal custody under the provisions of the Uniform Child Custody Jurisdiction and Enforcement Act. The Act was drafted in 1997 and has been adopted by 49 states, the District of Columbia, Guam and the US Virgin Islands. Massachusetts has not adopted it as of July, 2011. It was enacted in order to bring the Uniform Child Custody Act into Compliance with the Parental Kidnapping Prevention Act and other federal statutes such as the Violence Against Women Act. Any court that has issued a child custody order consistent with the Act has continuing jurisdiction over the case until there is evidence there is no longer a custodial parent in the state. In other words, if the custodial parent continues to reside in the state that issued the custody order, that state retains jurisdiction over the child. This example is a simplification of the provisions in the Act. There are many sections and you can read more at the related link.
Does she not have custody and seeks to gain it? Or does she want to ensure ongoing custody of a child in her care? Generally speaking, a birth mother has the better chance of achieving or retaining custody than the father, but various factors will be taken into consideration if the courts are involved. Also under consideration will be the suitability of either parent to have or obtain custody. Ultimately the courts should consider the welfare and comfort of the child, and so should the parents.
no
Under the Violence Against Women Act, he can't.
Basically no if the Father is an allies, he cannot stay in the country. He should process legal papers for the custody or else the custody might be given to the next of kin.