The cheekpiece is real but IMHO has been re-fitted to this rifle, & as you note, the wood to wood fit is not the best.
Concerning the front pad - it's not the pad itself, it's the milled flat area that the front pad sits on that is suspect. When Enfield, & Holland & Holland set up the UKproduced rifles originally they were done such that the scope in it's bracket would lie perfectly parallel to the rifle bore. This meant that a tiny depth of metal would need to be machined away from the receiver side wall so that the front pad located into position precisely. If you look at the receiver of an original 4T/L42 with its front pad removed you can see a 'window' a few thou in depth that conforms pretty precisely to the mating surface of the front pad. With the pad on, it is so precisely done as to be difficult to see, though it can usually be determined if you look carefully. In this case it looks like the the guy doing the milling had had a few too many Buds before he started.