Learn Spanish (Spain): Compro los cuadernos en la papelería. - I buy the notebooks at the stationery shop.

In Spanish, en is used for locations to mean "in", "on", or "at" a place. You use a when talking about movement or direction towards a destination (like going to the shop). Since the buying happens at the location, en is correct here.

Is a papelería the same thing as a bookstore?

No! A papelería is a stationery shop for items like notebooks, paper, and pens. A bookstore is a librería, and a library (where you borrow books) is a biblioteca. These are very common false friends for English speakers.

If I wanted to say "I buy notebooks" without "the", would I still use los?

No, if you mean "I buy (some) notebooks", you can just drop the article and say Compro cuadernos. By including los, you are referring to specific notebooks that both you and the listener already know about.

Why isn't the word yo (I) at the start of the sentence?

Spanish verbs change their endings depending on who is doing the action. The -o ending in compro already tells us that "I" am buying. You only need to add yo if you want to emphasize that you are doing it, rather than someone else.