What should I do about my feeling of dampness and the emission of foul odors with flatulence, and does that affect my ablution and prayer?

If you are certain that something has exited from you while passing wind, then you must perform Istinja (definition) (washing the private parts) and purify the area, then make Wudu for prayer. Otherwise, your prayer is not valid according to the majority of scholars. However, if it is merely an illusion or a whisper (Waswasa), then do not pay attention to it.