At our abattoir, Laverstoke in Hampshire, the net weight is the result of pay weight minus a fixed amount, almost aways -1.1, and listed as "Coefficient". So pay weight 58.0, coefficient -1.1 = net weight 56.9. Immediately above the net weight it says Tongue Out FFKD In, which means that flare fat and kidneys are still in, so I reckon that is what net weight is assumed to be, ie. the carcase minus tongue, flare fat and kidneys. Obviously they can't actually weigh the carcase like that as the kidneys and flare fat are still attached. When we collect our carcases, the weight shown on the ticket is the pay weight, and as we do our own butchering and weigh absolutely everything, including all the waste, bones, flare fat, kidneys etc., I would say pay weight is the more accurate weight for what you get back.
Don't have any additional information on the other things. Interesting that you are getting a "lean" measurement as well as back fat thickness, which we get listed as "Grade". Tamsaddle