@Anonymous I mentioned that I have used Keycheck with some of my longer-term guests. Most of my longer-term guests do not use Airbnb.
1) I ask the guest to complete the credit/criminal/background check as a prerequisite to the booking. I believe the cost is $29.
2) I have not had a long-term, international guest. I suppose your question would be relevant regardless of the checking method used.
3) If I were to use Keycheck in conjunction with Airbnb, I would require the guest to have the check done before the booking is confirmed. I do not use Instant Book.