Learn Hardcore Russian: Новый товар лежит на полке в магазине. - The new product is on the shelf in the store.

Russian doesn’t use definite or indefinite articles. Whether you mean “a new product” or “the new product” is understood from context or added words (e.g. этот товар for “this product,” какой-то товар for “some product”).

Why is товар in the nominative singular, even though it can mean “goods” in English (which is often plural)?

Here товар refers to a single item or a unit of merchandise. It stands as the subject of the sentence, so it’s in the nominative case. In Russian one often uses singular to talk about “merchandise” in general.

What case is полке in, and why?

Полке is in the prepositional (locative) case, singular feminine. After the preposition на, when you talk about location (“on” something), you use the prepositional case.

Why is в магазине using the prepositional case and not the accusative?

The preposition в can govern either accusative (for motion into) or prepositional (for static location). Since the sentence describes where the product lies (it’s not moving), we use prepositional: в магазине = “in the store.”

Why do we use the verb лежит here? Couldn’t we say находится or стоит instead?

лежит (from лежать) literally means “lies” and suggests the product is lying flat on the shelf.
находится (“is located”) is more neutral/formal and just states existence or location, without implying orientation.
стоит (“stands”) would imply the item is upright. Native speakers pick лежит if the shelf item is flat or laid out.

Why is the adjective новый not ending differently here? Shouldn’t it change for gender or number?

Новый is in the nominative masculine singular form, agreeing with товар (a masculine singular noun). Adjectives in Russian must match their nouns in gender, number, and case.

Is the word order in Новый товар лежит на полке в магазине fixed? Can I rearrange it?

Russian word order is relatively flexible. You could say:

На полке в магазине лежит новый товар. (Here you emphasize shelf/store location.)
В магазине на полке лежит новый товар.
The original S-V-A (Subject-Verb-Adverbial) order is neutral; moving elements changes focus or style but the meaning stays clear.

How do you pronounce магазине and товар correctly?

магазинé [məɡɐˈzʲinə] – stress on the second и.
товáр [tɐˈvar] – stress on the а.
Correct stress is important, as it can distinguish words.