Why did LaMia flight 2933 plan a flight longer than its listed fuel range? According to the wiki, the range of the airplane used in the LMI 2933 flight has a range of 1600 miles. The distance between the airports though is 1605 miles though. I presume the exact range varies on conditions, but why would a flight that is outside the listed range be planned? This seems like an amateur mistake that should have been quickly caught on pre-flight checks.

Also, the wiki states that before crashing the plane made 2 loops. If the flight was running out of fuel, why would they do this? It seems like the flight could have easily made it if they flew directly, and considering that they had declared an emergency the ATC wouldn't be able to say no.
The investigation is still on-going so I will stick to what is factually known. An airplane's range through the air should not be confused with travel over the ground, actual distance over the ground can vary significantly depending on the winds aloft. A significant tailwind will allow an airplane to travel farther than its listed maximum range, which is really just an estimate. We won't know what happened in this case until the investigation is complete. 

According to the information about the flight the pilot did not declare an emergency, so was told to orbit while another airplane which had a mechanical problem landed, this explains the loops.