The battery does come out, and the great thing is that all the batteries from some of the past few models fit! As for the card, get something that is fast. I picked up a Sandisc Extreme Pro 16gb with class 10 - go for the class 10 option of better with whatever card you decide on.
The battery does come out. Previous models had you remove the battery and place it in a charger to re-charge. The 820 allows you to keep the battery installed and simply plug it in to re-charge. The only downside I find is that, while the camera is charging, the door needs to remain open leaving it vulnerable to breakage in the event that it falls while charging.