What is the object of each preposition the new bakery opens in a week

In the sentence "the new bakery opens in a week" you only have the preposition IN. A prepositional phrase consists of preposition plus a noun, pronoun or gerund working as the object.

So, the prepositional phrase is "in a week", the object of the preposition is "week" (a noun) which is pre-modified by the indefinite article "a".