Yes to the battery, charger and instruction manual; no to a memory card. Also the instruction manual is very basic. However, many Sony Cybershots now come with handy in-camera instruction manuals; i believe this is one of them. If you want to verify what comes with a camera, you can often find unboxing videos on youtube, as well as individuals' reviews.
The camera comes with a batter, charger and instruction manual but no memory card. I don't know of any camera that comes with a memory card, that is always something that you have to purchase separately.