Yes.
Depends if it is a single trailer or a double-wide
not if she's married, or a single mother living in Arizona
Only if a single mother.
A single father, what does that mean? Are you divorced, ever married to the mother of your child, or is the child adopted by you, or is the mother dead or out of the picture? If your question is "How does a Father obtain residential custody after a divorce or in a paternity case", then I can answer this question. Let me know what your grounds for custody are. What is it about the mother or other parent that makes it harmful for the child to remain in their care?
First off, a single mother, regardless of status, has sole custody. The father has no assumed parental right, so he will be starting from scratch. Can he get custody? There's no more guarantee in this than for any single father. see link
Of course. Same general custody rules apply for a parent if in the military or not.
No. If the child's' mother calls the police you could loss custody of your child and possible go to jail. If I was you I would contact a lawyer who specializes in child custody cases. If you can get a notarized letter from the mother saying it is okay and giving you full custody.
If married, both parents. If single, the mother
Depends on the circumstances. If you are a single father, without court orders, the mother still has sole custody and control. If married, you have possession, however if you file for child support, you have a presumption of custody.
A single mother can as the US does not generally honor foreign father custody orders. Only Cuba does.
Based on reports from single fathers, the mother has sole custody until otherwise ruled on by the courts. see links
No, he has the same rights as single fathers, none until granted them.