Learn Hardcore Italian: In gioielleria ho visto una piccola gemma verde che brillava sotto la luce. - In the jewelry store I saw a small green gem that glittered under the light.

In Italian, many shops and public places pair in with the bare noun to express “in/at a …” generically. Examples include in banca, in chiesa, in università.
In gioielleria follows this pattern, meaning “at a jewelry store” in general. You could say alla gioielleria (“to/at the jewelry store”) when you refer to a specific one, but in gioielleria is more idiomatic for the general location.

Why is ho visto used (passato prossimo) instead of vidi or avevo visto?

The passato prossimo (ho visto) is the standard tense in spoken and most written Italian to indicate a completed action in the past.
• Vidi (passato remoto) is reserved for formal/written narratives or certain regions.
• Avevo visto (trapassato prossimo) describes an action completed before another past event, which isn’t needed here since there’s no earlier reference point.

In una piccola gemma verde, why is piccola placed before the noun and verde after?

Italian adjective order often reflects adjective type:

Size adjectives (like piccolo) typically go before the noun to highlight that quality.
Color adjectives (like verde) almost always go after the noun.
So una piccola gemma verde (“a small green gem”) follows the natural Italian order: size → noun → color.

What role does che play in che brillava sotto la luce? Could it be omitted or changed?

Che is a relative pronoun linking una piccola gemma verde (the antecedent) to brillava, introducing the relative clause. You cannot simply omit it—you need a connector. For a more formal style you could replace it with la quale:
una piccola gemma verde, la quale brillava sotto la luce

Why is brillava in the imperfect tense instead of ha brillato (passato prossimo)?

The imperfetto (brillava) describes an ongoing, continuous, or background action in the past. Here it paints a picture: the gem was shining under the light at that moment. Using ha brillato would suggest a single, completed shining event rather than that sustained glow.

Why does the sentence say sotto la luce? Why include la before luce?

When referring to a specific condition of “the light” shining on something, Italian uses the definite article. Sotto la luce literally means “under the light.”
Dropping the article (saying sotto luce) can occur in technical or stylistic phrases (e.g. osservare sotto luce polarizzata), but in everyday speech sotto la luce is the natural choice.