Are my prayers considered valid despite my suffering from chronic flatulence, urinary and fecal incontinence, and obsessive thoughts regarding purity and creed? And what is the ruling on the small amount of impurity I find after performing istinja (ritual cleansing after defecation or urination)? And is placing paper tissues on the penis and anus sufficient to ensure purity?

Determining whether a person is afflicted with سلس (incontinence/constant discharge) depends on knowing the continuous nature of the discharge from them. If the criterion for سلس applies to them, then they are considered to have سلس, and its rulings apply to them; otherwise, not. The presence of impurity stains around the anus indicates that the required purification (istinja') has not been achieved, and the area must be cleansed. It appears that the described suffering is caused by waswas (obsessive whispers), and staying in the bathroom for a long time and placing tissues on the private parts during ablution have not been commanded by the Shari'ah. The only way to find relief is to completely disregard and turn away from these waswas. When relieving oneself, one must perform good istinja' and then disregard waswas and excessive checking. As for waswas concerning creed, one should not pay attention to them but seek refuge in Allah the Almighty, and one's dislike of them is a sign of faith.