According to Amazon.com, you will receive a $30 credit applied to your credit card account within a few days of making your first purchase using that credit card. The $30 will credit will be reflected in your card statement. In terms of being charged interest, it depends on the APR which, as of now, ranges between 13.24% and 19.24%.
As with any other credit card, it is okay to close your account after you've paid off your balance but you should note that closing a credit card may hurt your score: http://www.filife.com/answers/will-closing-a-credit-/274

The 30$ rebate is credited later for the purpose of preventing people of opening the card and closing it right away just for that rebate. Also, its incentive to come back to amazon.com and purchase more using the 30$ credit. If you repay within the grace period, you will pay no interest. Also, IF you have other chase cards, before you close a card, transfer the remaining credit to your other chase card. This will not hurt your credit as bad as simply closing the account and loosing that avaliable credit.