Unless an order from the Reading Nook's online store is paid for by
the deadline indicated, the books cannot be shipped and the order will
be canceled.
PPs can be complement or modifier of a preposition, as in I stayed [until [after lunch] and [According [to Ed], it's a great car. But this is not the case in your example, where the PP by the deadline indicated is complement of the verb paid, not of the preposition for. In other words, paid has two separate PP complements: for and by the deadline indicated, where the latter is a temporal adjunct in clause structure.
The unless phrase is a conditional, equivalent to an if conditional with a negative protasis. Cf. If an order from the Reading Nook's online store is not paid for by the deadline indicated, the books cannot be shipped and the order will be cancelled.