Check your lens thread size which is beside a "ø" (diameter) symbol. Order this filter of the same size. 

Daa 1.8 FE has no OSS, therefore cheaper 

If the gh4 is a micro 4/3rds system then it will work. I have quite a few Nikon and Sigma lenses including the 50mm afs and they all fit and work perfectly. You will have to set your aperture and focus manually but the camera will make all the necessary exposure adjustments itself. Don't forget on a 4/3rds system your 50mm will be 100mm based on a full frame. Make sure your camera is a micro 4/3rds and not a 4/3rds, I have both. 

1. No, 82mm filters can only be bagged on 82mm lenses. 

You could try this tip. Hope it helps. Pan&tilt operation: Press the “pan/tilt” button on the upper right corner (A direction icon will appear in the middle of the screen when you press the “pan/tilt” button) →use the sound and brightness buttons to move the lens(The specific operation is shown in the video).