Is it obligatory for a worshiper who has an excuse due to flatulence to hold in the wind as it exits despite feeling its presence? Does its exit nullify ablution? And is it permissible to complete the Asr prayer if the time for Maghrib has begun?

If the emission of gas is continuous and does not stop for a time sufficient for ablution and prayer, this is called سلس ( سلس البول - سلس الريح ) and your ruling is to perform ablution for each prayer after its time has begun and to hasten to perform it. The emission of gas in this case does not invalidate the prayer or the ablution, and it is not obligatory to hold in the gas; rather, it is disliked to hold it in during prayer, even though the prayer remains valid. It is not permissible to delay the prayer beyond its time under the pretext of being busy with work; rather, it is obligatory to hasten to perform ablution and prayer at the beginning of its time. If you begin the 'Asr prayer and the time for Maghrib enters, complete your prayer, for it is valid according to the Malikis and Shafi'is.