While Guantanamo Bay has been unanimously assigned to American governing, I do not believe the Guantanamo Bay courts provide adequate judicial process. The whole essence of holding this facility outside of American borders is because they do not want to adhere to American regulations while incarcerating alleged terrorists. Without the rules of the United States, the Guantanamo Bay detention center does not, and most likely will not provide "adequate" judicial process.
No, it does not. Guantanamo was developed as a POW camp, designed to be a holding place for prisoners awaiting sentencing. However, research has shown that it clearly violates the Geneva Convention and is essentially a prison without due process. As a US prison, it houses mostly prisoners from outside the US, and treats them as prisoners of war. This exempts prisoners from just judicial process under US law.