I'm sorry about question that might llok stupid but I'm a newbee with disk brake

Look like The rotor is often 160mm Is the size of the rotor is important? is calipers are design for different rotor sizes or caliper can be adjust to the rotor size?
What'S about the lever. Do you have lever specific for disc brake. I know there is mechanical and hydrolic disk brake. I suppose the lever will be made for one or the other right. Will hydrolic work ok in winter?