Yes, it will fit any Sony e mount body, either full frame (a7..., a9...), or aps-c (like a6500, etc) 

For camera with telephoto zoom lens, you need to buy a tripod mount ring additionally or telephoto lens bracket for better balance) 

yes, i had no problems with infinity focus with this adapter. the only FD mount lens i use anymore with my sony is a vivitar 20mm, and i pretty much only shoot infinity focus with it. 

Yes it should work with the sony a6000. As long as the ka lens has an aperture ring on the lens and is not solely dependent on receiving aperture control from the body, this adapter should work fine with ka lenses. To my knowledge, there are no sony e mount to k mount adapters with electronic coupling so no lens control through the body (meaning aperture and focus are fully manual). 

The adapter will mount the lens and you will be able to use it manually. However, my copy of the adapter does not allow the lens to be fully mounted all the way until it clicks into place. It doesn't quite make it, but it's still very solidly mounted. Also, the manual aperture linkage doesn't work properly (on my copy, at least) so exposure is controlled only by shutter speed and/or ISO. You will be able to manually focus and zoom the lens but no VR, of course. It will be a frustrating experience. Instead, get a 14-140 Panasonic zoom if you can afford it!