1)
Why did they ask these three questions?
1.
Rashi (from Bava Basra 110a): There were astounding matters. Are you from the seed of Moshe, to whom was said "Al Tikrav Halom", "Mi Sam Peh" and "Mah Zeh b'Yadecha" (Shemos 3:5, 4:11, 4:2)?
2.
Malbim: They asked, who brought you from your house to here? What business do you have here? What are your wages?
2)
Rashi (from Bava Basra 110a) writes that they asked "are you from the seed of Moshe..." How did they know this?
1.
Malbim: They lodged near Michah's house and recognized his voice, because the Levi was from Kehas, whose cities were among Efrayim, Dan and Chatzi Menasheh (Yehoshua 21:5); this Levi was from a city of Dan.