1) That is the only code section that applies that I am aware of, therefore it is not allowed to run a flexible cord through a ceiling tile.
2) 1999 - Art. 250-118 describes what can be used as an equipment grounding conductor. I'm not old enough to have ever installed BX, but I'm thinking that it may fall under one of the categories listed as appropriate for an equipment grounding conductor,
3) I believe you have the correct section for this one also. As a rule, if the wires are there, even if they are dead, they have the potential of becoming hot at some point in the future. Therefore, I say that a box would be required.
