I use one on a Pentax 24-70mm filter size 82mm. Just make sure you buy the right size for your lens. I have the nd1000, and I am very happy with result. They also sell adaptor step down for your other lens. 

Yes. I have the same lens and adaptor on my Sony a7ll and it works beautifully. The m42 is also known as the 'universal' mount as other 3rd party camera and lenses also used it. I own 6 other K&F e-mount adaptors to different lens makers (ltm, MD, CF/CD, Nikon) and they all are well built with a nice snug fit. Highly recommended. 

67mm should also be stenciled on the front edge of the lens somewhere. If so, then you should be good to go. It should be on the lens because a lens cap can be lost or broken. 

The camea can take 1.6v rechargeable batteries, but in general rechargeable battery might drop its voltage quick depend on its physical performance. In the cold weather, recommend using Energize lithium batteries to get longer lifetime. 

I actually have not received this adapter yet. It's shipping from China. Don't think that was disclosed in the ad. However, I do not believe this is for the Pentax Q body rather for digital and film cameras that take the Pentax K mount in its many variations. So I'm expecting to be able to mount my Leica M mount lenses on my digital and film Pentax K mount cameras, no autofocus or relay of exposure information, only to be used with manual focus and exposure.