Learn Farsi: نخلستان در جنوب بیابان است. - The palm grove is in the south of the desert.

It is formed by combining نخل (nakhl), meaning "palm tree", with the suffix ـستان (-estan). This suffix denotes a place rich in or characterized by the root word. You have likely seen it in country names like افغانستان (Afghanistan, land of Afghans), but it is also used for natural features like کوهستان (koohestan, mountainous region) or گلستان (golestan, rose garden).

What is the difference between بیابان (biyaban) and کویر (kavir), since both can translate to "desert"?

While often used interchangeably in casual speech, they have geographical distinctions. بیابان refers to a dry, arid region with very little rainfall and sparse vegetation, like a typical sand or dirt desert. کویر, on the other hand, specifically refers to a salt desert or salt pan, like the famous Dasht-e Kavir in Iran, which is mostly barren clay and salt.

There is no visible connecting word between "south" and "desert" in the Farsi text. How are they linked?

They are connected by the ezafe vowel (an invisible "e" sound), making the pronunciation jonub-e biyaban. When specifying compass directions relative to a place, you link the direction (like جنوب, south) directly to the landmark with the ezafe, which acts similarly to "of" in English.

Does در جنوب بیابان mean the grove is inside the southern part of the desert, or further south outside of it?

Grammatically, the ezafe construction جنوبِ بیابان (south of the desert) combined with the preposition (in) implies it is located in the southern part of the desert itself. However, in casual everyday speech, native speakers sometimes use this exact same phrasing to mean something is located just south of the desert's borders. You would rely on context to know if it is inside or outside.