It does come with a battery charger. It is easy to pop the battery out of the phone and plug it in to the small battery that conveniently plugs into any available electrical outlet. I don't know yet about the memory card question. Memory cards are relatively inexpensive, so I just bought an extra to be sure.
It does have a charger, plus the battery lasts longer than others I've had. I have not been able to store even one picture w/out a memory card. But if it can, I just haven't figured it out. I like the camera, but, even with the higher megapixels, the pictures don't look any better than my older 8 megapixel casio. I would say to try out others and test them for yourself. I admit I am not the best with electronics.
It does come with a battery charger, but I'm not sure how many pictures you can store on th memory card as I usually print my pictures before I get very many on the card and then store them on a CD and erase the ones on the memory card.