If I have a bunch of creatures face down with morph, but they've been turned up before to be turned back down by an effect, can I switch my cards around so my opponents don't know which card is which?
No
707.6. If you control multiple face-down spells or face-down permanents, you must ensure at all times that your face-down spells and permanents can be easily differentiated from each other. This includes, but is not limited to, knowing the order spells were cast, the order that face-down permanents entered the battlefield, which creature attacked last turn, and any other differences between face-down spells or permanents. Common methods for distinguishing between face-down objects include using counters or dice to mark the different objects, or clearly placing those objects in order on the table.
Darn. Okay, thanks! :)
One of the main reasons for this is summoning sickness. During my khans prerelease someone tried cheating by attacking with a morph summoned the turn it came in