Is the prayer of one who follows Sheikh Ibn Uthaymeen in believing that a woman's passing invalidates the prayer rendered void? And is praying towards a sitting or reclining woman beyond the sutra (barrier) forbidden?

The madhhab of Shaykh Ibn 'Uthaymeen is that prayer is قطع (interrupted/invalidated) by the مرور (passing) of a woman in front of the worshipper, whether the worshipper is a man or a woman. However, extending a hand or a leg, or similar actions, is not considered مرور (passing), and prayer is not interrupted by it. This is based on the action of the Prophet (peace be upon him) with 'A'ishah (may Allah be pleased with her), where she would sleep in front of him with her legs in his qiblah. When he prostrated, he would nudge her, and she would withdraw her legs. Therefore, if the prayer is not invalidated with a woman in front of the worshipper, it is even more fitting that it is not invalidated if she is behind his sutrah.