Is ablution (wudu') after ghusl (ritual bath) following menstruation valid if the sniffing of water into the nose (istingshaq) is omitted from it? Is drying oneself between them considered a mistake? And is it obligatory to remove the white accumulations on the teeth for the ablution to be complete?

The preponderant view is that rinsing the mouth and sniffing water into the nose (madmada and istinshaq) are obligatory in both ablution (wudu) and ritual bathing (ghusl). The ghusl for major impurity (hadath akbar) is sufficient in place of wudu, provided that madmada and istinshaq are performed within it. Scholars have differed on the obligation of consecutive performance (muwalat) in ghusl, but the preferred opinion is that it is a condition for its validity. As for the white residue on teeth resulting from food particles, it does not invalidate wudu or ghusl, though its removal is better.