The name of Marco Inaros' ship is the Pella. Pella was the capital of the ancient Macedon Kingdom and birthplace of Alexander the Great.
The UN Penitentiary is actually the R.C. Harris Water Treatment Plant in Toronto, Canada. It has been used in many films and television shows. The area surrounding it has been modified with CGI. In reality, around the plant is many many houses, not a forest of trees.
Gaugamela was the location of an ancient battle in 331 BC where Alexander the Great defeated King Darius III, thereby conquering the Achaemenid Empire. The village was located in what is now northern Iraq, near the modern city of Erbil.
Inside the UN Penitentiary (actually a Toronto water treatment plant and architectural treasure, as noted elsewhere on this page), the visitor lobby/security gate area is actually the Old Toronto Stock Exchange trading floor, dressed up very little for this episode. It's preserved as a heritage property -- an architectural masterpiece, blending streamlined modern, art deco and stripped classicism. I'm pretty sure the murals in the background are the originals currently onsite, with no modifications.
The Chef on UN Force One is Chef Casey. This might be a nod to Steven Seagal's character in Under Siege (1992) who was a former Navy SEAL named Casey Ryback who served on the U.S.S. Missouri as the captain's personal chef. Chef Casey winds up saving the President, who is visiting the ship as it is the Navy's last battleship and is about to be decommissioned, when it is attacked by terrorists who plan on stealing the ship and taking the President hostage.