From when do we mention the powers of rain? R' Eliezer says: From the first Yom Tov of the festival. R' Yehoshua says: From the last Yom Tov of the festival.  R' Yehoshua said to him: Since rain is but a symptom of curse during the festival, why mention [it]?  R' Eliezer replied to him: I, too, did not say to re-quest [rain], but [merely] to mention “He causes the wind to blow and the rain to fall,” in its proper season.  He responded: If so, one should always mention [the powers of rain]!

He who leads the services on the Yom Tov of Rosh Hashanah, the second [chazzan] causes the shofar to be blown; but when Hallel is said, the first chazzan recites the Hallel.

For the shofar of Rosh Hashanah, they may not go beyond the Sabbath boundary, nor may they remove a heap [of stones or debris] for it, nor may they climb a tree, nor may they ride an animal, nor may they swim on the water, nor may they sever [it], whether with an implement that is prohibited under Rabbinic law or with an implement that is prohibited by the Torah [through a negative commandment]. But if one wishes to put water or wine into it, he may do so.  One should not prevent the children from blowing the shofar; rather, one may occupy himself with them until they learn [to blow].  One who practices has not discharged his obligation, and one who hears [the shofar being blown] from one who practices has not discharged his obligation.

The order of the shofar blasts are three [sets] of three [blasts] each. The duration of a tekiah is like three teruos. The duration of a teruah is like three quavers.  If one blew the first [tekiah] and prolonged the second [tekiah] for the duration of two [tekios] —- it counts as only one.  If one recited the blessings and later a shofar became available to him, he should blow tekiah-teruah-tekiah three times.  Just as the chazzan is obligated, so is every individual obligated.  Rabban Gamliel says: The chazzan discharges the congregation’s obligation.