Being somewhat general, here's some common causes for each problem you've given
Chain comes off - because its too slack. Try loosening the rear wheel nuts and slide the whole wheel backward a bit. The chain has to have some slack, but not enough to let it fall off either side.
Pedals are not turning - The pedal cage (bit the foot presses against) should rotate around the pedal axle reasonably freely. It may or may not coast if spun, but it should turn around smoothly. If not, the pedals may be faulty.
OR you might have meant: Crank is not turning on the bottom bracket - this would be bad - a new bike would have the crank installed in the box. You shouldn't have to fit a crank to a frame yourself. If that's not turning freely, something's really wrong.
Rear hub brake rubs Are you sure the wheel is centered in the frame? Its possible the tyre is rubbing on the chainstay or seatstay. Loosen the wheel nut on one side and push/hold the rim to a central position between the stays, and retighten.
I see that this bike has a center-mounted drink bottle cage over the rear wheel. Check its not rubbing on the tyre either. Finally check the training wheels haven't pressed some part of the chain cover into the wheel hub.
Rear hub brake doesn't come on when pressed The coaster brake should never need servicing, and would absolutely come pre-assembled. Sounds like the bike might have some problems. Given its a $109 USD BSO, it might be better to return it right now under your local consumer rights.