What hint can we find in the context of the two verses the Gemara cites, that the first refers to Rosh Hashanah that falls on Shabbos, and the second refers to Rosh Hashanah on a weekday?

Why is the stated concern of the Gemara that one might carry the Shofar four Amos within the Reshus ha'Rabim - rather than that he might bring out the Shofar from a Reshus ha'Yachid to the Reshus ha'Rabim?

The decree not to blow Shofar on Shabbos must be applied universally, even in locations where carrying is not a concern (e.g., a private courtyard or one with an Eruv Chatzeros). As such, why did R' Yochanan ben Zakai allow Shofar in those cities with a Beis Din?

Nowadays, when we do not blow Shofar on Shabbos, is it considered Muktzeh? To what degree?

During ancient times, in what locations was the Shofar blown on Shabbos, and during what eras?

Why was Shofar blown on Shabbos (after the Churban), only in the presence of Beis Din? What level of Beis Din was required?

Why, in the times of the Beis Hamikdash, was Shofar on Shabbos limited to the Mikdash, as opposed to Lulav (when its first day fell on Shabbos), which was fulfilled everywhere? After the Churban, on the other hand, R' Yochanan Ben Zakai perpetuated the observance of Shofar on Shabbos - but not that of Lulav!

On a deeper level, why is Shofar not blown on Shabbos - except in the Mikdash, where it is blown?