No. Additionally, Tennessee does not have firing squad as a listed method of execution.

TCA § 40-23-114

(b) Any person who commits an offense prior to January 1, 1999, for which the person is sentenced to the punishment of death may elect to be executed by electrocution by signing a written waiver waiving the right to be executed by lethal injection.

That's her only option, outside of the savings clause in (d) which permits any other method if all other methods listed are unconstitutional.

Also for your other question, yes. Things like espionage, high treason, aid and comfort to the enemy, large scale drug trafficking, etc... But usually if it isn't because you murder someone, it has to be that you've done something really bad. Like if you gave tactical blueprints of thermonuclear devices employed by the United States to North Korea and the blueprints for the vehicle to deliver those devices, yeah, that's getting up there.