Is it necessary to make sure that no wady has come out during prayer, knowing that it exits continuously before and after urination?

It is not obligatory to search for the exit of wady. It is sufficient to act upon the default, which is that nothing has exited. If wady exits continuously, then if you know of a time when its exit ceases before the prayer time expires, you should wait and pray with a valid purification. However, if its exit does not cease, then your ruling is that of one afflicted with incontinence (sahib al-salas): you perform ablution after the entry of the prayer time, and you pray the obligatory prayer and whatever supererogatory prayers you wish after taking precautionary measures.