Who are our Avos?

The gemara in Brachos 16b asks why you can only call Avraham, Yitzchok and Yaakov the avos and nobody else. I have a few questions:

1. What's the point of being called one of the avos?
2. What does it mean that you can't call anyone else an av - the next line of the gemara says that everyone was called abba besides slaves?
3. Why is it only coming to exclude the shevatim (as Rashi points out and is evident from the next line of the gemara) - what about Noach and Adam?
4. Was the hava amina that all 12 shevatim should be counted giving us a total of 15 avos or that each person would only have 4 avos?
5. A lot of people do know what shevet they're from - all Kohanim and Leviim so why does the gemara think that it could be the reason they're not counted is because we don't know where we're from?
6. What is the gemara's answer because they're chashuv? The gemara didn't realize that right from the beginning? If not then why didn't it ask why we wouldn't list Terach?
7. Is the gemara saying in the maskana that chashivus is the only criteria even if they're not necessarily our forefather? It seems that way because we only list Rochel and Leah and many Jews (ok not so many nowadays) did not come from either one of them. Presumably the gemara is saying that Rochel and Leah are still their imahos and not Bilha and Zilpa.
8. Are Avraham, Yitzchok and Yaakov considered the avos of geirim who may not have come from any of them?

I think that the gemara knew the entire time that the avos and imahos would only be from the people who are responsible for starting the Jewish people. There was never a hava amina that we should go further back than Avraham nor did the gemara ever consider that we should go beyond the shvatim. It's true that we've had great leaders like Moshe Rabeinu but he wasn't a father of the people. Avraham was clearly the first forefather but the question is only who exactly was the last.

The gemara's original statement was, "Nobody can be called the fathers of Yisrael besides ..." That's how Rashi explains it. So the gemara asks why the shevatim can't be called avos also. Obviously, one of them is each of our forefathers but that isn't what we need. We want to know if they are fathers of Klal Yisrael. The gemara suggested that it might be because you need the combination of being literally our forefather and being a shaper and founder of Yisrael. The gemara says that's obviously not true because Rochel and Leah are both counted even though we're not all from either one of them (and many of us are from neither). So the gemara concludes that it has nothing to do with lineage. It only depends on who is important as a father of Yisrael. The gemara is saying that nobody else can be called an av of Yisrael but there's nothing wrong with me calling Yehuda my forefather.