Is it permissible to marry another man after being divorced three times by the first husband, knowing that the first two divorces were revocable and the third was irrevocable, and that the husband did not reconcile during the waiting period?

If your waiting period (iddah) has expired after a divorce, whether it was a revocable (raj'i) or irrevocable (ba'in) divorce, you have the right to marry anyone who proposes to you. If there is a dispute concerning the divorce or reconciliation, the Sharia court is the authority to resolve these disputes.