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The rules don't specify this, but I assume that you do, because if you played them both at the same time, then a disc which is next to both of them can't figure out which polarity it's supposed to be, and if the two discs are next to each other, then they implode on themselves upon trying to determine their own polarity.
I would also assume, then, that you can play the two discs in either order you wish?
First let me start by saying that I haven't been on BGG in a while, had some health issues. That being said, I just caught wind of this thread.
The answer to all your questions are, yes.