What is the ruling on one who finds the taste of toothpaste or food after rinsing more than 10 or 20 times while fasting, and how many times should one rinse so as not to be excessive?

What you mentioned about the taste of toothpaste lingering in the mouth after rinsing is an exaggeration stemming from waswasah (obsessive whispering/doubts). If you rinse your mouth after using toothpaste until you are reasonably certain its taste has gone, then there is no harm in swallowing your saliva. However, if you are certain that the taste of toothpaste remains, then do not swallow your saliva that contains it. It is preferable to avoid using it during the daytime in Ramadan.