I can't get my new 520 chain on, even with the adjuster fully slack. Should the 520 chain have more links than the 525?

no 520 simply refers to the width of the chain it has nothing to do with the length, Go on the B&C Express website and find out how many links a standard chain has for a NC30 running stock gearing, then count your links.

If you have the same number of links as suggested at B&C Express then either your running daft gearing (different sprockets) or your doing something wrong (Not really sure what you can do wrong if im honest)

Where is your hub adjuster positioned, as you look at the bike from the right (Throttle) side where is the adjuster located top middle being 12 oclock and bottom middle being 6 oclock.

done it for you, should be 104 link chain!

104 on std sprockets should be alright, but I've usually gone 106 as I am cool

Have you ever serviced the hub adjuster and do you know it is in the right way up? It might have some shit in it preventing the proper adjustment which killed off your last chain..?

Can you turn the hub 90deg in each direction with the chain off?
You said there was not enough adjustment to tighten your worn chain, I then suggested the hub was seized.
Now you say not enough adjustment for a new chain. I still say hub is seized.
Remove and clean /grease and refit the hub.

Can't fit hub upside down ,the chain would be tight on the underside of the swinging arm and run slack on the top of it, but adjustment would be the same.