According to
Wikipedia, India has a bicameral parliament operating under a Westminster-style parliamentary system.
The President of India is the head of state, elected indirectly by an electoral college. The Prime Minister is head of government and exercises most executive powers. The PM is appointed by the president.
Prahtibha Patil is the current president. Dr. Manmohan Singh is the current PM.
The president of India is the supreme commander of Indian Armed Forces.
Since independence, the federal government has mostly been under the control of the Indian National Congress (INC).
Not sure what the police are called, but it seems they all operate under the umbrella of the Indian Police Service (IPS).
You can find a lot of information through Wikipedia. Hope that helps.