Does one have to inspect and insert a finger into the anus before prayer to ensure that no flatus has been released due to defecation, given the presence of urinary incontinence, obsessive-compulsive disorder, and weakness in the excretory muscles resulting from a previous act?

The cure for obsessive thoughts is to ignore them and pay them no mind. You should live your life normally. Do not search for feces, and do not enter the lavatory except when necessary. When relieving yourself, wash the area until you are reasonably certain of its purity, and reasonable certainty is sufficient for you. If you have relieved yourself and cleansed, do not worry about obsessive thoughts thereafter. If you are certain of suffering from incontinence, perform ablution after the prayer time has begun and pray the obligatory and supererogatory prayers with this ablution until the time expires.