1) If the type of error was taharah. The tawaf of umrah was invalid because he became certain that he had not performed wudu for tawaf of umrah and realised after leaving makkah but he is certain he performed wudu for tawafun nisa. so he did not have wudu at the time of tawaf of umrah, 2 rakat salat of tawaf of umrah, saiy and taqseer but he had wudhu for tawafun nisa and 2 rakat of tawafun nisa of umrah.

Can he assume still assume that his wife is halal for him and that he is not in ihram?

Yes, and you should delegate someone to complete the invalidated acts for you