Why did they answer the second question first?
Malbim: They could not answer the first question. They were still unsure if this was Hashgachah or chance - "v'Im Lo v'Yadanu Ki Lo Yado Nag'ah Banu" (verse 9). They would test this [via sending the Aron with cows]. They did know, if we will send it, it may not be empty.
What is "Asham"?
Rashi: It is something to show admission of doing improperly to it.
Radak: It is an atonement for what you did.
Why did they say "Az Teraf'u"?
Malbim: If we send it empty, Hashem will not strike us further, but He will not be appeased to heal those already stricken.
What will they know after they are healed?
Rashi: They will know that Hashem afflicted them. There is no reason not to be healed after they return it.
Radak: They will know why Hashem did not remove His hand from striking them, because they were keeping the Aron with them.
Malbim: Even if the gift does not avert His anger, surely He will inform you via your prophets and Kosmim the reason for His anger, and what else we can do to avert it.
