Since no one has seceeded from the US, there is no civil war, so the US is still not at war with Jose Padilla. In the same way the the US was not at war with the Oklahoma bomber, despite him bombing a federal building. He is not a member of the US military, so court martial shouldn't apply.

Even if he is a combatant, he is a POW by default until determined to be unlawful by trial, then he can be convicted by civilian laws. As opposed to his indefinite detention without trial.

The US President is now allowed to use necessary and appropriate force. 'Necessary and appropriate' does not suggest the President is allowed to ignore existing case law. Unless the Senate has the power to amend the Constitution without stating that they're doing it.

Even if they can, that still means you should 'Run!'. Someone accused of being a terrorist has no way of challenging this (unless they have political infuence). Don't convert to Islam.