digital zoom. 

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

HI your fujinon m42 55mm 1.8 and a sigma-z m42 135mm 2.8 are M42 mount, the item can fit your camera and lens 

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! 

Yes, 4x zoom.