https://en.wikipedia.org/wiki/Military_tribunals_in_the_United_States
Anons read through that when you get a chance.
How do you introduce evidence legally?
Military courts are allowed to suspend certain rights protected by the Constitution when it comes to military members.
What about enemy combatants?
If it is ruled that their right to privacy can be suspended due to being an enemy combatant then NSA data collection could be legally introduced if I'm reading this correctly.
Oh, and appeals?
Well it depends either it is going to be handled by the CAAF which is a board of civilian judges appointed by POTUS or the SCOTUS! Win. Win.