Northern Kurdish

No — they're separate Kurdish languages, related but not mutually intelligible. Kurmanji preserves grammatical gender (masculine/feminine), keeps an ezafe-like construction inherited from older Iranian, and uses different ergative-marking strategies than Sorani. Speakers of one need real study to follow the other. Both are Kurdish, but the gap between them is comparable to that between major Romance languages.

Yes, two: masculine and feminine. Articles, demonstratives, and adjectives mark the gender of the noun, and the ezafe linker (a clitic that connects nouns to their modifiers) takes different forms depending on the noun's gender and number. Sorani has dropped this system entirely, which is one of the major grammatical splits between the two Kurdish languages.

Primarily a Latin alphabet (Hawar) developed in the 1930s by Celadet Bedirxan, used in Turkey, Syria, and the Kurdish diaspora across Europe. In Iraq, Kurmanji is written in Perso-Arabic, the same script tradition as Sorani. In Iran, also Perso-Arabic. Soviet-era Armenia historically used Cyrillic for Kurmanji. The same word can look entirely different on the page across these scripts.

Southeastern Turkey is the largest Kurmanji-speaking region by population. Northern Syria (Rojava) has a substantial Kurmanji-speaking population with active institutional support since 2012. Iraqi Kurdistan's northern regions (Duhok province) speak Kurmanji rather than Sorani. Northwestern Iran (especially West Azerbaijan province) has Kurmanji communities. Diaspora populations in Germany, France, the United Kingdom, Sweden, and the United States are large.

Variable. In Turkey, Kurmanji is the dominant Kurdish language but has experienced restrictive policies, with broadcasting and education bans gradually loosened over the past two decades. In Iraq, Kurmanji shares co-official status with Sorani in the Kurdistan Region. In Syria's Rojava region, Kurmanji is used in local administration and education. Iran does not use it in formal education.