What is the status of the child of Cohen and divorced woman? Is there any possibility for this kind of marriage?
There is a Torah commandment prohibiting the marriage of a Cohen and a divorcee. The marriage is however valid after the fact- in other words if the divorcee wife decides to leave her husband to marry someone else, she requires a "get" (=a halachic divorce) from her husband, the Cohen. The children of such a marriage are not "mamzerim" (=bastards) but are challalim, a special status.