Final answer:
Jawaharlal Nehru was India's first Prime Minister, and the country operates under a presidential-parliamentary system, with the President serving as the head of state and the Prime Minister as the head of the government.
Step-by-step explanation:
India's first Prime Minister was Jawaharlal Nehru, a key figure in the country's struggle for independence and subsequent shaping of the Indian state. Nehru assumed office on August 15, 1947, the day India gained independence from British colonial rule. As for the type of government, India has a presidential-parliamentary system, a hybrid known more informally as a parliamentary democracy. In this system, the President serves as the head of state, while the Prime Minister acts as the head of the government. The Indian government is characterized by a dual executive setup, with both a democratically elected Parliament, which selects the Prime Minister, and a President who is elected by an electoral college.