You need a letter from the other parent giving permission. Otherwise you risk having difficulty either leaving or returning.
Custody is having the protective care or guardianship of someone or something.
There is no creature called a "marsupial dragon". Anyone who tries to tell you otherwise is "having a go" at you (an Australian colloquialism for teasing).
When married you have equal rights to the child.
Does she want custody or access?
Full custody is defined as one parent of a child having sole control over a minor child with the other having no custodial rights. Primary custody means that both parents share custody (also known as joint custody) but the primary custodian is the parent that the child spends most fo their time with/lives with on a regular basis. In other words, the parent that is not the primary custodian is the one that has the visitation rights.
If you live in the US... The child having the father's last name has NOTHING to do with custody. If Dad is listed on the birth certificate as the father, then both parents have equal custodial rights until a court declares otherwise--you need a custody order. If Dad is not listed on the birth certificate, it will be a simple thing for him to petition the court to establish paternity and once that's done he can then petition for custody/visitation.
no, having joint custody gives you more control than having power of attorney.
you can sign the custody over to her or she could go to a judge and try to prove you unfit to take care of them and prove her having custody in their best interest
Someone with duties to watch, or having custody, is a "guardian".
No, a man does not always get custody. If one of the people in a marriage has an affair, it is usually the person not having an affair that gets custody of the child or children.For example, if the husband is having an affair, and the wife wants a divorce, the woman (wife) would get the custody of the child or children, and not the man (husband). This is the same vice versa, too.
Believe me if she knew she would be having a talk with you. I do suggest that you pick the right time and discuss this with your mother. If anyone would understand most mothers do.