She can't unilaterally declassify anything so if another agency sent something classified to her, she could not lower the classification.
If something came from one of the intelligence agencies that was Secret or Top Secret, it would not be sent over the open internet to her public email. That would be a security violation on the part of the sender.
Classified items were sent to her to her private email address. Her server, which she had setup for herself, contained those classified items. That is against the law. It is also against the law to handle classified items in a way that puts them at risk.
She is responsible for the content of her server, and therefore broke the law. That she somehow didn't recognize classified material isn't a defense. The people who sent her the classified materials also broke the law (especially since they may have removed any classified markings from the documents).
If something is not marked properly, the receiver doesn't automatically get a security violation.
False. Not on materials created by the CIA, NSA, etc. She would have no authority on those, and those are what everything is about.