Tested with Nikon Z 7 and Nikor 14-30mm Sline, dark corners are not obvious for 14mm and no dark corners for 16mm. 

Yes 

1. If there is ever any more than a slight amount of rotational play, you may want to try tightening the lens mount adapter so it will hold the lens tighter to the mount. There are 3 flanges in the middle of the adapter (what the lens locks onto) that are split open slightly, this gap is what gives the tension that holds the lens tight to the body. Over time and with use these gaps decrease in size, no longer pulling the lens tight to the adapter, which allows the lens to move inside the mount more than it should.
2. To tighten the fit, get a slim metal object (a #1.5 or #2.0 small flat eyeglass screwdriver is ideal) and insert it into the slit to open it up just a little bit (see images below, make sure to do it to all 3 evenly). The more you open the gap, the tighter the lens will be to the adapter; too much and the lens will have a hard time mounting so make sure to do it just a little bit at a time to all 3 flanges evenly, it doesn’t take much at all to get a tight fit.Note: please do not use too much strength, or the shrapnel will be damaged.

 

I don't think you need any. There is no glass. 

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!