You have a lot of questions. Usually the court orders 2-3 appraisals and a value will be determined. If party who wants to keep the property can't buy the other two out, then (since it can't physically be split), the property will be ordered to be sold and the proceeds split (less expenses). The court may opt to appoint a receiver for this process. Obviously it is much less expensive for the parties to agree because costs could be substantial.