Whales and dolphins only sleep with half of their brain at a time due to their need to come to the surface to breathe; they don't breathe automatically like humans do. If someone really tranquilized an orca like Nolan did with the needle in the harpoon, both halves of its brain would be asleep at the same time and therefore it would stop breathing. It wouldn't have survived for as long as Nolan's harpooned orca did.
Orcas aren't actually monogamous, they don't stay with one mate for life. That belief stemmed from the fact that the same male orcas travel with the same females, but it was later discovered that male orcas stay in their family unit (pod) with their mothers, sisters, aunts, etc for their entire lives. Females from one pod mate with males from other pods to decrease the chances of inbreeding.
The goof items below may give away important plot points.
When Orca attacks Ken, it's seen that the orca grabs Ken's arm with its jaws, and then drags him into the water. However in the shot where orca drags Ken into the water, the Orca has nothing in its jaws, and Ken is nowhere to be found. This hints that a video of an orca jumping and splashing was used to complete the effect.