noise figure is actually (i/p snr)/(o/p snr).....its ideal value is 1 although in practical, it is greater than 1.....
when you try to measure the noise figure, you would optimize the circuit in such a way that maximum power gets transferred from i/p to o/p.....
50 ohm is just a standard in rf for terminating impedances.....although some people use 75 ohms even now......
when you have your rin=50 and rout=50, maximum power will be getting tranferred from the input to the output load.....
also the maximum signal in terms of peak to peak will be coming at the output when you terminate the output imepedance at 50 ohms.....