If there is another parent listed on the birth certificate, and has any sort of visitation to the child, then this may very well be a 'No'. You will need to speak to a lawyer in your area to get more specific information in regards to this question.
If the parents are married, yes. If one parent has sole custody that parent can consent.
No.
Depends on who made the change. If the parents are not married to each other the decision what last name the child will have belongs to the mother and she will not need the consent of the father.
As the law stands you can work in a non-skilled job from the age of 16, without your parents consent.
18. 16 WITH parent consent.
No, you will need the other parents and the courts permission.
Well I got one at 14 in Spain without even parents consent =]
To get married without parents consent is 18 in most States in the United States as 18 is no longer a minor.
Yes as long as you are of adult age you can leave if you want. If you have the children with you you will most likely need their other parents consent.
Parental consent is not required for emancipation. The court has to agree and the parent's opinion in the matter are likely to factor in.
Nothing, if they don't know.
I get the feeling they are not married. if there are court orders for custody, visitation and child support she can not do this without the other parents consent and the courts consent. Otherwise she will be breaking the courts orders which is illegal.