Is suffering from excessive flatulence and frequent doubt about passing wind and invalidating ablution, and doubt about the number of rak’ahs and prostrations, considered an excuse that permits performing ablution once for each prayer? And is it permissible for a woman to wear socks and wipe over them with this doubt?

There is no cure for obsessive-compulsive disorder (waswas) except to ignore it. So, whenever you doubt that something has exited or that you have forgotten a pillar [of prayer], do not pay attention to this doubt. Continue with your purification (tahara) and prayer. Purity is not nullified by doubting the emission of wind; the original state is the continuation of purity. If you are certain that something has exited, then perform ablution (wudu'). If the emission of wind is continuous, then perform ablution for each prayer after its time has begun, and pray both the obligatory (fard) and supererogatory (nawafil) prayers with this ablution.