1)
What did the lottery determine?
1.
Rashi: How much everyone will bring.
2.
Malbim: This is like it says in Ta'anis 28a (that when Bnei ha'Golah ascended, they did not find wood in the chamber of wood. Certain families offered their own. It was enacted that they bring every year, at particular times.
2)
What is "Korban ha'Etzim"?
1.
Rashi: An offering of wood for the Ma'arachah (woodpile) on the Mizbe'ach.
2.
Ibn Ezra: There were times for Kohanim, Leviyim and the Am to cut and bring wood.
3)
Why is it called Beis Avoseinu?
