Is my prayer valid in the following cases: 1. Upon hearing a sound whose source I do not know (whether from my stomach or from the private parts) while waiting for Fajr prayer, and I am in a state of ablution, without feeling anything exiting, and I did not repeat the ablution? 2. When I stepped on something with my foot during ablution and I do not know whether it is impurity or not, and I forgot to look at it and repeated the ablution and prayed? 3. After finishing Witr prayer, some wind exited from me, and I do not remember whether I prayed Fajr without ablution or not?

The questions indicate the presence of waswasa (whispers/obsessive thoughts). It is advised to ignore these waswasa and turn away from them. Ablution (wudu') is not nullified except by a firm certainty that something has exited. Doubt does not nullify purity. The default state of things is purity, so it is not necessary to wash the foot if something touched it, unless one is certain that it is ritually impure (najis). If one is certain that ablution has been nullified but doubts whether they performed a new ablution, the default state is the continuation of the ritual impurity, unless this doubt is due to waswasa, in which case one must ignore it.