Does masturbating during the daytime in Ramadan invalidate the fast and necessitate making up the missed days (qada') and offering expiation (kaffarah), given that one cannot recall the number of times this was done out of ignorance? And what is the ruling on a man touching a woman during the daytime in Ramadan without ejaculation?

We ask Allah to accept your repentance, guide your steps, and accept your good deeds. If you live in cities where there are people of knowledge (fiqh), then you have no excuse for ignorance. You must estimate the number of days you broke your fast by masturbation and make them up. You also owe expiation for delaying the make-up until another Ramadan arrived, which is feeding a poor person a mudd of food (approximately 750 grams) for each day. What you did with that girl does not invalidate the fast as long as nothing was emitted from you, but you must offer sincere repentance.