Does swallowing saliva that has gathered on the lips after wetting them with the tongue invalidate the fast, whether done out of ignorance of the ruling or not, and does this necessitate making up the fast or offering expiation?

The best cure for obsessive thoughts (waswas) is to ignore them and pay no attention to them. Merely moistening the lips with saliva does not invalidate the fast unless one deliberately swallows it, knowing that it invalidates the fast. There is no harm in a fasting person wiping his lips with his tongue or a wet tissue, as long as he does not intentionally swallow the wetness, and he is not required to wipe again. The default is the validity of an act of worship, and this certainty is not removed except by another certainty. So, unless one is certain that something has entered their stomach, their fast is valid. Abandoning prayer due to obsessive thoughts is a grave matter and a violation of Allah's command. The person afflicted with waswas must pray and not pay attention to doubts.