Learn Russian: Внизу работает магазин.

In Russian, the most important or "new" information usually goes at the end of a sentence. By putting магазин last, it introduces the shop as a new piece of information. This is why it translates to "a shop" rather than "the shop". If the sentence was Магазин работает внизу, it would mean "The shop is open downstairs."

Why does the sentence use работает (works) instead of a word for "open"?

While you can say a shop is открыт (open), it is very common and natural in Russian to use работать (to work) to describe a business, institution, or machine that is currently functioning or open for business.

Could I use вниз instead of внизу here?

No, because внизу answers the question "where?" (где?) and indicates a static location (downstairs or below). Вниз answers the question "to where?" (куда?) and implies motion, like walking down the stairs. Since the shop is just sitting in one location, you must use внизу.

What is the difference between внизу and под?