Is it permissible for individual heirs to participate in the public auction for the sale of the property, and is it a requirement to go to court due to the presence of a minor among the heirs?

If the heirs are adult and of sound mind, they are permitted to agree on any method of division, even if it means one of them receives less than their share. They are also permitted to sell the property to one of them at any price they agree upon. However, if there are minor heirs, the property may not be sold except at the highest price it can fetch, and it is forbidden to show favoritism to anyone in its sale. This is because the guardian of a minor must act in the minor's best interest, and it is forbidden for him to show favoritism with the minor's wealth. Otherwise, he will be liable for any shortfall, due to Allah’s saying: ﴿And do not approach the orphan’s property except in a way that is best.﴾ Therefore, if an auction does not lead to the highest price, it is not valid as a means of appraising the property. If it does lead to the highest price, the heirs are obligated to refer the matter to the court, which will appraise the property through its experts to safeguard the minor's right.