What is the ruling on one who constantly suffers from the emission of foul-smelling gas; must he renew his ablution every time it is emitted, and do congregational and Friday prayers become waived for him?

If a worshiper doubts that something was emitted during prayer, he should not interrupt it unless he is certain that something was emitted. The emission of gases has two scenarios: either it has a time when it stops, in which case you should perform ablution and pray during the time it stops. Or it is continuous, in which case you perform ablution for each prayer after its time has begun, and what is emitted during prayer does not harm you. As for going to the mosque with this wind present, it is not permissible because it harms the worshipers and the angels.