What is the maximum current that can run through a Freedom board without the board burning?
Do you refer to the board itself as if an electrical current were to magically circulate through the board; to the maximum current provided by a specific pin in a component? your questions is too general, you need to re formulate your question and be more specific.
Regarding power supply input. I have a 12V source that I am planning on converting down to 5V, but I do not know the current supplied so I want to be sure I will not burn my board
The voltage regulator in the FRDM boards is NCP1117ST33T3G, its maximum rated output current is 1000mA; you can use that figure as a milestone.