The Golem: Plenty? I know of 2, neither of which were documented well at all.
Old Man: No offense intended, because I have great respect for you, but I am going to call you out on something here. It is a flaw in the current rationalist thought that it is taken too far. Judaism (for the most part) believes in the supernatural. Thus, unless you want to claim to be an entirely Maimonidean rationalist (which I don’t think anyone is nowadays, but I guess you have what to rely on if that’s what you claim), you have taken rationalism too far. The Gemara is full of stories of the supernatural. Unless you want to say (like the Rambam) that every single one was a Mashal or something like that, there is no reason to deny the existence of a Golem. See also SHU”T Chacham Tzvi Siman 63 (maybe 93?), if I recall correctly.