It can effectively reduce reflection on the filter surface and reduce ghosting and other problems. 

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. 

Hello! The camera has electronic anti-shake function, but it is not waterproof. 

In the pictures, I notice at least no disturbing reflections. Always remember that lenses can produce something like this even without a filter, especially in backlight, for example when the sun is low in the sky. 

Yes, that's possible with my lenses.