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A pad is always appear in one side of board.
As for question 3, Eagle won't turn component pads into vias.
If you have your double-sided PCB plated through all pads act
as vias. On a non plated PCB soldering a lead top and bottom
creates a via.
For your question 1, pads can not be used as vias. If the board is double-sided and pads are plated they can be considered to be vias as well.
They are normally part of a component.
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