Though the display refuses to show greek characters. Is there any support/upgrade for unicode characters in ID3?

Currently the player does not support unicode characters. However, some people have been able to edit the player's fonts so that it will display non-US characters in the extended ASCII character set, so it's possible someone might be able to make a Greek font for you. Anyone up to the task?

If I connect the hard drive of Rio Player to my desktop computer using the appropriate cable for laptop hard drives, will I be able to manage my mp3's?

No. The management must be done by the player software in conjunction with Emplode, Emptool, or JEmplode.

If you are not satisfied with the speed of the USB cable, you should try ethernet, it's faster. It should be plenty fast for pretty much any music management you need to do.
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Tony Fabris