I think so. Excerpt from the operating instructions: "Use the micro USB cable to transfer data or to charge the battery. Use Bluetooth to establish a connection with another KidiZoom Snap Touch camera. You can send messages, photos or voice recordings or play games together."

No, I don't think wireless headphones work. This was definitely not possible with my granddaughters, but that was two years ago. Here is an excerpt from other forums about the product:
Additionally, it has a microSD card slot and a headphone jack, so it is compatible with appropriate memory cards and wired headphones.
The VTech KidiZoom Snap Touch camera supports Bluetooth, but mainly for the connection between two cameras to share messages, photos or voice recordings or to play games together. There is no clear indication that wireless headphones can be connected directly via Bluetooth.