Is it obligatory for someone from whom a liquid is discharged or who sweats from the anus, and smells the odor of feces without their presence, to perform ablution and pray for each prayer, or is he required to wash his anus every time he wants to perform ablution for prayer?

If it is merely a doubt or a whisper (waswasa) regarding something exiting from the posterior, then it should be disregarded, and the default is that nothing has exited. The mere sweating of the area is pure and does not invalidate ablution. However, if you are certain that secretions have exited from the posterior, then it is obligatory to perform istinja' (cleansing) from them, purify whatever has touched the body and clothes, and perform ablution for prayer. If this occurs daily, then according to the Malikis, it is not obligatory to remove that impurity.