What is the significance of the third month?
Malbim: The harvest 1 began then; they made piles of Bikurim.
Shavu'os, in the third month, is "Bikurei Ketzir Chitim" (Shemos 34:22). The barley harvest begins in Nisan (Rashi Shmuel II, 21:9)! Perhaps not so many people plant barley, so it was not enough to make piles. (PF)
What is the meaning of "Hechalu ha'Aremos Li'ysod"?
'Rashi': The beginning of a matter is called Yesod, like Yesod ha'Bayis, which is the beginning of the building. We find in Ezra (7:9) "Hu Yesod ha'Ma'aleh."
Radak: The Yesod of the piles is their purpose. Li'ysod is Mekor (infinitive).
Why did they finish in the seventh month?
Malbim: This is when they finish gathering [produce from the fields]; the Terumos and Ma'aseros finished.


