What is the ruling regarding past prayers and fasts if the ghusl was invalid due to ignorance of the necessity to wash certain body parts, or due to not conveying water to the roots of thick hair? And what is the correct intention if multiple causes for ghusl converge?

The cure for obsessive thoughts is to ignore them. In ghusl (ritual bath), a strong presumption of having thoroughly washed is sufficient; certainty is not required. Doubts about an act of worship after completing it are to be disregarded. If you become certain that a part of what must be washed was not reached by water, then your ghusl is invalid. Your fast is valid because purity is not a condition for the validity of fasting. It is permissible to act upon the easier opinion as long as you are afflicted with obsessive thoughts. If multiple events occur, all of which require the same type of purification, one ghusl is sufficient.