An out-and-back course runs in one direction to a turnaround point, then retraces the exact same route back to the start and finish. It's popular because it only needs one road corridor closed and a single start and finish area. Runners typically cross paths with the leaders and the back of the pack along the way.
It's a route that heads out along one road to a turnaround point, then comes straight back along the same road to the finish. The start and finish are usually at, or very near, the same spot.
They're logistically simpler, needing only one road corridor closed and one finish line setup. It also makes spectating easier since you'll see runners pass twice, once heading out and once coming back.
Not inherently, but seeing faster runners already heading back can be a mental challenge for some. Others find it motivating, since you can gauge exactly how far ahead the leaders are.
Not necessarily, they follow whatever terrain the road offers, so hills on the way out become hills again on the way back. Check the elevation profile rather than assuming based on the format.
Running the same stretch of road twice can feel repetitive compared to a route with constantly changing scenery. Traffic at the turnaround point can also cause brief congestion in a crowded field.