It HAS an Auto Focus button. Works great! As for the Anti-vibration/shake, NO, not that I can see. However, a hand stabilizer handle should help with that. I haven't notice any vibrations although I'm still experimenting. Beautiful video! FYI,Can't find an external monitor that works with this camera. Purchased two different monitors and five different HDMI Cables, No luck. But the flip out built-in is fine. Good quality, I just wanted something larger. 

It takes a 3.7V lithium ion polymer battery. You recharge it by plugging in the camera. The camera comes with 2 batteries (one extra since it only needs one). 

Dear customer: This construction time-lapse camera is a waterproof and dustproof integrated design, and the rating is IP66, so you don't need to protect items such as cases. Hope our answer is helpful to you. 

Yes, it charges them quickly and then the light for that slot turns green. To me, that's an indication that it's going to lose power because the battery isn't hot the next day. (No, they don't need to be charged overnight, they're fast.) 

Simply connect the USB cable to the charging case