In Minnesota, children under the age of 18 years old cannot pick which parent to live with.  The Court does not delegate to a minor what is in their best interests.

No.  If you decide to move out of the home that you shared with your spouse during the marriage, it does not effect your right to marital property.

No.  There are two types of custody the court must award:  Legal custody which has nothing to do with the amount of time the child is with you but gives you an equal say in major decisions about the child like where they will attend school.  There is a presumption of an award of joint legal custody unless there has been domestic abuse between the parents.  The second type of custody is physical custody.  This is where the child's residence will be.  Unlike legal custody, there is no presumption for or against joint physical custody.  Joint physical custody does not mean equal 50 50 each automatically either.  Parties can have joint physical custody with one parent having the child in their care 30% of the time and the other parent 70%.  The issue usually pertains to parenting time and the number of overnights in a year the child will spend with each parent.  This is because it directly impacts child support.  If parents are awarded equal 50 50 parenting time, this will significantly reduce the amount of child support one party may owe to the other.

The answer depends on whether or not the parents were married at the time of the child's birth or not.  Married father's have rights at birth.  They have every right to take their child with them without the wife being present if he was married to the mother at time of birth.  Unmarried fathers do not have any legal or physical custody right to a child born to a mother who was not married to them at the time of the birth.  Unmarried father's have no visitation rights automatically either.   Unmarried father's MUST obtain a court order signed by the judge which specifically grants them custody and visitation right.

Court is always involved as divorce or custody is a court action which requires a judge to sign a written order making the terms legally enforceable.  Legal pleadings must be prepared, served and filed with the court to start a divorce or custody action. The parties usually participate in mediation and attend mediation with their own lawyers to try to reach an agreement.  It is not recommended to attend mediation without your own lawyer present, as how can a party agree to anything without first knowing what their legal rights are and if the agreement is fair?  If an agreement is reached in mediation, before the end of the session, it is put into writing and signed by both parties and both lawyers.  However, this does not conclude the action, as the agreement terms must be incorporated into a court order that is signed by the judge.