Is it permissible to perform ablution (wudu') and prayer (salat) while feeling the emission of wind (gas) during them, and is it permissible to perform them without holding back the wind in this situation?

If you feel that gas has been discharged during wudu' (ablution) or salat (prayer), do not pay attention to it unless you are certain of its discharge, in which case wudu' is nullified and salat becomes invalid. If the discharge of gas is continuous, it is considered akin to incontinence (sals). In this case, you should perform wudu' for each prayer after its time has begun, and what is discharged will not harm you. You may then perform the obligatory prayer (fard) and as many supererogatory prayers (nawafil) as you wish until the time for that prayer expires. However, if there is a time when the discharge stops, wait until it stops, then perform wudu' and pray.

As for holding back gas, if it is due to incontinence, there is no benefit in holding it back. If it is not due to incontinence, it is better for someone who wishes to pray and needs to relieve themself of gas to do so first. This is based on the saying of the Prophet, peace and blessings be upon him: "No prayer should be performed in the presence of food, nor when one is resisting the two impure things (feces and urine)," narrated by Muslim. The prayer of someone resisting (the discharge) is valid, though disliked. However, if one becomes certain of the discharge of gas, their prayer is invalidated, unless they are someone suffering from gas incontinence.