I will be arriving on an intra-European flight into Hamburg at 540pm.

It appears that I can take a train directly from the airport at 630pm or so and then transfers at the main Hamburg station for a train to Berlin.

Is the 50 minutes sufficient? This seems to be very straightforward. I can buy the ticket online for 73 Euro but not sure if that is refundable in case of a misconnect.

Am I OK to buy from a machine or on the train instead, or am I better off buying ahead of time (any way to buy it lower rather than 73 Euro)?

Finally, what are my best options to buy a 2G or 5G micro-sim data card for my IPAD2 (United States ATT variety), and can I buy the card at the Hamburg airport, main Berlin train station or at the Zoogarten terminal?

Thanks in advance for any help/suggestions!