Mork and Mindy, Laverne and Shirley, Joni Love Cachi and Happy Days all took place in the same universe (the previous three all spining off from Happy Days, though Mork only appeared in Happy Days as a dream and obviously took place many years after Happy Days.)
Negative, Mork was NOT a dream on Happy Days.
he was dreaming, after he woke up from his nap he heard a radio report talking about a flying saucer really being a weather balloon. Right after this Robin Williams shows up knocking at the door asking for directions to a highway, Richie wigs out and Robin Williams leaves.
Outside on the porch, it's revealed that Robin Williams really WAS Mork, since he starts talking to Orson and telling him about the 1950s. Orson then tells Mork that he'll be visiting 1978 next.