Can I use Jynx's "Mimic" attack to draw cards from my deck when I don't have any cards in my hand?
Yes, but you must shuffle your deck first before you draw.
Source: HeartGold & SoulSilver FAQ (2010-02-11), PUI Rules Team (2010-02-11)
Can I use Jynx's "Mimic" attack to shuffle my hand into my deck when my opponent has no cards in his or her hand?
Yes, but you won't draw any cards after you shuffle it in.
Source: HeartGold & SoulSilver FAQ (2010-02-11), PUI Rules Team (2010-02-11)