concerning the second part of your question: yes, you can go to the city, but you need to go through passport control (assuming your passport allows you to enter the Schengen area) before exiting the airport and of course you have to go through security and passport control when you come back. There are also lockers in the train station. This might be a safer choice, in case your TK flight leaves from D, which is unlikely to be clear when your flight from the US arrives.