Rebbetzin et. al.,
1. Did you look up my reference to Kiddushin 71b? You can go on Sefaria, press “A” and get an English translation. Due to widespread aveirot during the First Temple period and the fact that mamzerut is forever we cannot know who today is a mamzer and who is not. Statistically today we might all be. Argumentative people (except cohanim) are especially suspect.
2. Actually just about all mamzerim can be freed of the stain if enough digging is done. For example, a witness who regularly does an aveira (tax evasion, smoking) is disqualified. Rav Moshe once annulled a first marriage after his investigators discovered that the bride had been undergoing psychiatric treatment and had the din of a shottah.
3. Were the Jews in Bavel considered Yidden being that they did not speak Yiddish?