As strange as this may sound, LAN traffic, meaning traffic between two devices on the local area network, never passes through the router - even without a switch.
You may think of the router as a single device, but, consumer routers are actually as many as three devices in a single casing - a router, a switch, and a wireless access point - and the only time traffic passes through the router is if it's moving to/from the internet.
With regard transfer speeds - the discussion cannot be had in isolation - files are transferred from one device to another and over a connection, the file transfer will be as fast as the slowest of these three - you've described one, so there's no way to know if it's normal - I will tell you this though, the DNS-323 is no speedster, there are probably more complaints about slow transfer speeds than any other problem.