Although this product is equipped with LAN terminal, can I share music files between the unit and the computer by connecting the computer or DJ unit via LAN?

You can share music files by directly sending the music files or management data of rekordbox (Mac/Windows) stored on the computer to the XDJ-RX. This sharing of files is called 'rekordbox Link Export'. It saves the efforts of writing music files on a USB device.
You cannot share music files with other DJ units, even if those devices are connected by LAN.