Learn Polish: Gdzie jest to małe zaplecze? - Where is this small backroom?

No, it has a much broader use. While in this sentence it likely means a physical room behind a shop or restaurant, zaplecze is often used figuratively to mean facilities, backing, or logistics. For example, zaplecze techniczne refers to technical support or technical facilities.

Is there a trick to remembering the word zaplecze based on how it is built?

Yes! It literally translates to the area behind the back. It is formed from the prefix za- (behind) and the root of the noun plecy (back). This makes it very logical that it refers to a backroom, backstage, or background support.

Why do we use to małe here instead of ten mały or ta mała?

The word zaplecze is a neuter noun, which is typical for Polish nouns ending in -e. Because of this, the demonstrative pronoun to and the adjective małe must also be in their neuter singular forms to agree with the noun.

Since our current lesson is about the distributive po- prefix with plural objects, how would I say: Where did you close up all these small backrooms?

You would first need the plural form of the noun, which is zaplecza. Then, you would use a distributive verb like pozamykać (to close multiple things one by one). Assuming you are speaking to a man, the question would be: Gdzie pozamykałeś te małe zaplecza?