On the first question: there are different schools of thought, but generally there are instructions the judge reads to the panel before they retire for deliberations, including an admonition against he use of unlawful influence by any panel member.
On the second question, I’m not sure what current policy is, but the UCMJ still says a CM is a public proceeding and is only closed for the taking of classified evidence or highly sensitive testimony,AND must be reopened immediately afterward. I don’t know whether that section would trump a lack of authorization to enter the federal reservation.
Thanks much for the info,folks.