Why do the B'rachos begin specifically with rain?
Ramban: Because when the rain falls in the right time, the air is pure, the fountains and rivers produce good water, and the land 1 yields a bountiful harvest and the trees a lot of fruit. 2 As a result of all this, the people remain healthy, they and the animals do not lose their babies and they live long lives. 3
Ramban: Incorporating the animals, the birds, the fish ... , like we find often in Tanach - See for example, Bereishis, 1:1, 2:1.
Ramban: As the Pasuk goes on to explain.
Ramban: Consequently, it is the greatest of all the B'rachos.
Why does the Torah write "Gishmeichem" ? your rain?
Sifra: In order to extrapolate "Gishmeichem", 've'Lo Gishmei Kol ha'Aratzos' - to teach us that (due to the seasonal rain), there will be plenty in Eretz Yisrael and (due to a lack of rain), there will be a shortage of food in all the other lands, and they will come to Eretz Yisrael to purchase food and enrich its inhabitants.
What are the implications of "be'Itam"?
Rashi (citing Ta'anis, 22b #1): It implies in the ideal time - on Tuesday night and Friday night, when people are not in the streets. 1
Targum Onkelos and Targum Yonasan: It implies that the early rain and the late rain will fall when they are due.
Ta'anis, 22b #2: It implies 'average' (just right) -not too too little and not too much. 2
What is the definition of "Eitz ha'Sadeh"?
Rashi: It means 'non fruit-bearing trees'. 1
Which will bear fruit in the time of Mashi'ach -when the current B'rachos will take place (See Sifsei Chachamim).
QUESTIONS ON RASHI
Rashi writes that "Eitz ha'Sedeh" means barren trees. But "Piryo" implies that they normally bear fruit!
Moshav Zekenim: Perhaps "Piryo" refers to the field - the trees will produce what the field nmormally produces.