Gemara Review BEITZAH 9A

What is the basic disagreement between Beis Hillel BH and Beis Shammai BS in the mishna?

What do both Beis Hillel and Beis Shammai agree on in the first mishna?

Is Rav Chanan a Tanna or an Amora? What situation does he say the machlokes BH and BS is in the mishna?

Why, according to Rav Chanan, are BH and BS arguing in the mishna? Why does each side have its opinion? What's their reasoning?

What do BH and BS both agree on in the mishna, according to Rav Chanan, and why?

The Gemara says איני and introduces Rav Yehuda/Rav. What does איני mean? What principle does Rav hold by and how is this a contradiction to Rav Chanan?

Why does the Gemara feel it can ask a question by Rav on Rav Chanan? Aren't they both Amoras? How does Rashi explain this?

The Gemara answers תנאי היא. What does this phrase mean, and how does this help Rav Chanan (answer in general, then do the next follow-up question)

How does the baraisa dealing with drenched clothes on Shabbos help support Rav Chanan? Who does Rav go like?

What does איכא דאמרי mean?