Dreaming

AFAIK. To get luna put a bed in your house and lie on it. I dont think there are any special unlock requirements.. I've had a quick Google :)

Oh and u need switch online membership.. :)

Yes, and anything you can lie on coutns as a bed, like sleeping bags and such

But it has to be in your house to work like Eliza said

Any bed will work, but you need to acquire a total of 5 neighbors before Luna sends you an invitation in the mail.