Kurdish

Linguistically distinct enough that most modern descriptions treat them as separate languages within a Kurdish dialect cluster. Kurmanji preserves grammatical gender; Sorani has dropped it. Sorani uses ergative past constructions; Kurmanji has different past-tense morphology. They share a common Iranian ancestor and Kurdish identity but are not fully mutually intelligible without exposure.

Multiple, depending on country. Turkey and Syria use a Latin alphabet (Hawar) developed in the 1930s. Iraq uses a modified Perso-Arabic script for Sorani. Iran uses Perso-Arabic for both Kurmanji and Sorani communities. Armenian Kurds historically used Cyrillic. The same Kurdish word can look entirely different on the page depending on which Kurdish region's script is in use.

The historical Kurdish region (Kurdistan) spans southeastern Turkey, northern Iraq, northwestern Iran, and parts of northern Syria — collectively home to most Kurdish speakers. Smaller communities exist in Armenia, Lebanon, and the diaspora across Germany, France, the United Kingdom, the United States, and Sweden. The Iraqi Kurdistan Region is the only territory where Kurdish has full administrative autonomy.

Yes — both Iranian languages, though in different subgroups. Kurdish is Northwestern Iranian; Persian is Southwestern Iranian. They share grammatical structure and many cognates but are not mutually intelligible. Persian speakers tend to find Kurdish more accessible than the other way round, partly because Persian-language education in Iran exposes Persian speakers to less Kurdish than vice versa.

Iraq recognizes Kurdish (specifically Sorani) as a co-official national language with Arabic. Iran recognizes Kurdish as a regional language but doesn't use it in education. Turkey lifted the most restrictive bans on Kurdish broadcasting and education over the past two decades, but Kurdish has no official status. Syria's Kurdish-controlled territories use Kurdish in local administration.