My appologies, we use BNC for 50 Ohm aerials on shipping. 75Ohm is usually a Coax Connector.
As long as the connection is good, the housing maintains the impedance. Personally I prefer solder but if carried out correctly, it makes no difference.
It makes no difference to the impedance. BNC are often a combination of solder and compression, but you get crimp types too. Crimp is probably better for production line assembly and solder/clamp better for DIY.
The 'thicker central pin' claim is often made, but many deny it. There was a long debate about this a few years ago. I can't remember whether it was on here or a UK vintage radio site. I think the concensus was that the pins are supposed to be the same size, and the change in impedance is obtained by using less dielectric in a 75 ohm socket.