In the U.S., Is it ever legal for an aircraft to occupy the runway turnaround area while another is taking off or landing?
Jim's answer is accurate. Unless there is a proper boundary between the turnaround and the runway, an aircraft should not be there while other aircraft are landing or taking off.

In the FAA's AC about airport design:


  Obstacle Free Zone (OFZ). The OFZ is the three-dimensional airspace along the runway and extended runway centerline that is required to be clear of obstacles for protection for aircraft landing or taking off from the runway and for missed approaches.


The dimensions of the zone are different depending on the aircraft size and approach minimums. Specifically the runway OFZ has widths from 120 to 400 feet. This is the zone typically protected by the hold lines (pictured in Jim's answer), which are typically placed to provide adequate separation for the worst anticipated case at that airport.

Regarding the edge markings, they should be parallel to each other and not follow the edge of a turnaround pad. From the AC on airport markings:


  When a taxiway connects to a runway or the runway has turn pads or turnarounds, the runway edge marking remains continuous between the runway and these adjoining infrastructures.


If the turnaround pad is designed to be occupied while the runway is in use, this is referred to as a holding bay. A proper holding bay would look like this:



This illustration comes from the airport design AC. Notice that the FAA considers this poor, because it provides no guidance such as taxiway center lines for pilots to follow.