Do the 2013 Time Capsules work as a NAS drive? Can I partition the 2013 Time Capsules to use some of their storage as a network drive?
No. The internal drive gets shared as one volume. You would need to layer user access controls to set up folders for different uses within the same share.

But you can attach an external drive to the USB port and access that as shared storage from any peripheral on your network. Those show up as separate volumes when you use the stock Apple firmware on the Time Capsule.