What is the ruling on doubting the emission of discharge and doubting the invalidation of ablution because of it, and what is the ruling on one who pours water on part of the foot and wipes over the rest when performing ablution?

You must continue to resist intrusive thoughts (waswas). The discharges that exit from a woman's vagina (vaginal moisture) are pure, according to the preponderant opinion, but they invalidate wudu' according to the majority of scholars if you are certain of their exit. As for doubt, wudu' is not invalidated, and there is no need to inspect to confirm. Doubts should be ignored until certain conviction is attained. It is permissible to adopt the weaker opinion that they do not invalidate wudu' if the intrusive thoughts are severe. Correct istinja' is achieved by washing the impure area with water until it becomes rough again, and the predominant impression of cleansing is sufficient; there is no need to go along with intrusive thoughts. Similarly, for wudu', the predominant impression that water has reached the obligatory parts is sufficient.