If you mean by "loose trigger," that it "flops" back and forth when the rifle is cocked, or not, but fires when you take up the slack, then that is the design of the trigger mechanism.
I don't know about the "Happy Trigger," but others probably will.
As for a receiver sight, I am not sure of the 336s of that '57 vintage, but look on the left side just in front of the hammer and see if there are two small holes with tiny screws in the receiver. If so, those are there to mount a receiver, or "peep" sight.
Williams makes their 5D receiver sight that fits there and Lyman makes one for same. Williams is a bit cheaper, but the Lyman is a more easily adjusted peep sight. Also, you can sometimes find the older (discontinued) Redfield receiver sights for the 336 (Or Win. 94) at gun shows, and they are good ones too.
I prefer my Marlins to Winchesters... but that is just me.
Good luck.
L.W.