Your PCM is located by your left foot with the connector sticking thru the firewall (It's the longer skinny one). The IDM is mounted just just below the driver's side hood hinge.
A breakout box is a diagnostic tool that plugs in between the PCM and connector and lets you check the voltage signals with a multimeter or if only the harness side is connected, the continuity of the circuits. It "breaks out" the connections for you.
Also, an injector breakout box (actually a misnomer, should be called a cutout box) installs between the engine harness and the body harness and has switches to allow you to turn off injectors individually.