From India, you will need to take a flight to either Sydney or Melbourne (Sydney is directly connected to New Delhi), and then take another flight to coastal cities of Queensland such as Port Douglas and Cairns. From their, various tours will take you to the reef.
Like many countries, the application for the Australian visa is also handled by VFS Global. All Indian passport holders can apply for the Australian visa, and all the documents required to complete the visa application are listed on their website.
From nearby cities. Discuss routes maybe. Talk about ease of rental for cabs / self driven cars
From nearby cities. Talk about connectivity, compare different services (if any)
Getting around on the reef can only be done via waterways. Boats are available in number and it's easy to find one for wherever you're headed.