What are the implications of this divorce regarding the 'iddah (waiting period) and maintenance, knowing that the wife received her Mahr five years ago and insists on the custody of the three young children?

You divorced your wife with the third divorce, so she is irrevocably separated from you, and she must observe the waiting period (iddah): three menstrual cycles, or three months, or until she delivers if she is pregnant.

Nafaqah (financial support) and housing for the divorced woman during the iddah: If she is pregnant: She is entitled to nafaqah and housing until she delivers. If she is not pregnant: The preponderant opinion among us is that she is not entitled to nafaqah or housing.

Custody of children: A boy, after reaching the age of seven, is given a choice between his parents. A girl, after reaching the age of seven, stays with her father. It is a condition for the custodian that there be no impediment, such as فسق (moral transgression). The Sharia judge arbitrates custody disputes in cases of contention.