I've heard that there are ways to speed up Mist Energy regeneration, such as by certain chat commands or by simply logging off for a while. Even if this is by a minute amount, this is pretty good to use, like a 5% increase while offline, similar to the WoW rest system.
Is this true, or simply unfounded rumours?
Completely unfounded. ME will always take about 13 minutes each to regenerate and 22 hours to fully regenerate.
http://wiki.spiralknights.com/Energy