What should I do about my doubt regarding my fasting certain days of Ramadan in my youth, and my committing a sin that invalidates the fast, which I do not remember if it was during a daytime in Ramadan?

As long as the matter is merely a doubt and a whisper concerning the validity of the fast or whether something has invalidated it, then there is nothing upon you. The default is the validity of the fast and the clearance of one's responsibility, for doubt after completing an act of worship has no effect. Just as repentance from a sin erases its trace, Allah accepts repentance from His servants no matter how great their sins.