No clue, I would either try it or ask amazon. Their page just says verified checking account. So I don't know if that counts.
Certainly, it is possible to have a routing and account number at the same time. In fact, prepaid debit cards might be less expensive than having a checking account. This is particularly true if you carry a low balance.
Yes, you can. Prepaid credit cards are a different story, but you can typically make ACH deposits on a rechargeable prepaid debit card.