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.
Can a preposition modifies a prepositional phrase like the above sentence? I have learned that preposition phrases are adverbs or adjectives and prepositions modify nouns only.
I don't know enough to answer the question in the title, but I'm making a post anyway because this is not a case of a preposition modifying a prepositional phrase.
The sentence that you quote is an example of a "prepositional passive". The equivalent sentence in the active voice would be of the form "Unless [someone] pays for an order from the Reading Nook's online store by the deadline indicated, the books cannot be shipped and the order will be canceled."
I hope this makes it clear that the prepositional phrase starting with "by" modifies the verb "pays".
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.
