Is it permissible to make up missed prayers or perform current prayers by gesturing during prostration, due to involuntary gas expulsion at the time of prostration and after repeatedly performing ablution and attempting to get rid of the gases?

We ask Allah to grant you healing and well-being. The remedy for the whispers (waswas) of gas expulsion is to disregard them and pay them no mind. If it is merely a doubt, do not give it any attention and continue with your prayer. As for the missed prayers, since you have repented for them, repentance wipes away what came before it. There is no harm in adopting the opinion of those who do not consider their qada' (making up) obligatory, in order to alleviate hardship. If you are certain that gas is being expelled during prostration, then your ruling is that of one afflicted with incontinence (sahib al-salas). In this case, you should perform wudu for each prayer after its time has begun, and what exits from you will not harm your prayer. The matter is easy: if it is a doubt, disregard it; if it is a certainty, then your ruling is that of one afflicted with incontinence. And if you wish to make up what you missed as a precautionary measure, that would not be difficult for you.