520, 525, 530, etc., is an international reference number used to identify a given chain or sprocket. A 520 or 525 chain/sprocket (both suitable for use on the 1299) share the same pitch (the distance from the centerline of one chain pin to the centerline of the next chain pin, in the case of a chain). However, the inner width/pin length of 520 and 525 chains differ... the sprockets are dissimilar as well.
In the case of a street driven bike, a heavy duty 525 chain and steel sprockets will provide years of reliable service. While 520 components will save some weight, the 525 components, in most cases, tend to be the stronger of the two.
A 41T rear sprocket will pick up the low end a bit and shave a bit off of the top end... however, it's a reasonable choice for a street driven bike.
There's wear that can easily be observed, and then there's wear that may be less discernible. Regardless of either, best practice calls for the chain and both sprockets to be replaced as a set so as to maximize the service life of the new components. The components wear as a set and should be replaced as a set.
Removal and installation... as the old chain will be discarded, a hand grinder with a cutoff disc attached can be use to remove the old chain. Depending on the manufacturer of the new chain, you may have options regarding the type of master link to use. EK Chains ZVX3 Heavy Duty 525 chain, for example, can be installed using a rivet type or screw type master link. The screw type link is suitable for bikes displacing as much as 1400 cc's. Only a single open-end wrench and a pair of pliers are required to install the screw type link... no special tools required.
If you're working with OEM components, you may want to take the opportunity and install a quick-change rear carrier. There won't be any additional work required as the final drive will have to be removed in it's entirety to replace the OEM components, and the cost of a new rear quick-change sprocket and sprocket carrier will be nearly identical to that of an OEM replacement. The original cush drives pins and carrier flange can be retained and installed with the quick-change sprocket and carrier. Replacing the chain and sprockets will then be easier the next time around.
A link regarding the same: BREAKING IT DOWN, THE 1199 FILES, THE CHAIN AND SPROCKETS