Short answers, pulled from the story.
The Muslim conquests of Afghanistan began in the 7th century, accelerating after the battle of Nahavand in 642 AD. Fifteen years after that battle, Arab forces controlled all Sasanian domains except parts of Afghanistan, Tabaristan, and Makran. Full Islamization was not achieved until the 10th-12th centuries under the Ghaznavid and Ghurid dynasties.
The Zunbils were rulers of Zabulistan and Zamindawar, the region stretching between Ghazni and Bost. They acted as a barrier against Muslim expansion for nearly two centuries by using the inhospitable terrain to trap Arab armies, luring invaders into barren valleys and cutting off their food supplies. The last Zunbil was killed by Ya'qub ibn al-Layth al-Saffar in 865.
The Army of Destruction, known as Jaish al-Fana, was an Arab force dispatched in 698 by al-Hajjaj, governor of Iraq and the East, with orders to destroy the Zunbils' strongholds and enslave their progeny. The campaign ended in catastrophic defeat; only 5,000 soldiers survived, the rest perishing in what sources call the Desert of Bust, most likely the Registan Desert.
Buddhism, Hinduism, and Zoroastrianism all flourished in the region before the Muslim conquest, alongside locally developed traditions. Tokharistan (Bactria) was the only area conquered by Arabs where Buddhism had heavily flourished. Kabul and Zabulistan housed Buddhism and other Indian religions, while the Zunbils of Zamindawar maintained a shrine to the god Zun linked to Hindu and Tibetan religious practices.
Kabul's decisive conversion came in stages over several centuries. Caliph Al-Ma'mun (r. 813-833 AD) mounted the last Arab campaign against Kabul, capturing its king and converting him to Islam. The Hindu Shahi dynasty that subsequently controlled the area was defeated by Mahmud of Ghazni, who reigned from 998 to 1030 and encouraged mass conversions in Afghanistan and India.
The Nuristanis, known as the Kafir people of Kafiristan, were the last to be converted. They practiced a form of ancient Hinduism infused with locally developed accretions and remained politically independent until Afghan Amir Abdul Rahman Khan conquered and converted them in 1895-1896.