Is there any way to set this camera to take time lapse photos or super-long exposures (4-6 hrs)?

i'm not sure about that particular camera....but most compact digitals don't go past 15....and the dSLRs only go to 30 or so without bulb...

Nope....and if you do succeed, be advised that any shot of the moon that is longer than 1/30 of a second will result in a blur due to the earth's rotation in conjunction with the moon's rotation around the earth.