India did not have a national anthem at the time of its independence. Rabindranath Tagore wrote the song Bharoto Bhagyo Bidhata in 1911; it was renamed "Jan Gan Man" and declared the national anthem of India by the Constituent Assembly on January 24, 1950.
Mahatma Gandhi did not participate in the first Indian Independence Day celebrations in Delhi. He was on a hunger strike in kolkata, trying to put a stop the bloodshed brought on by partition.
Lord Mountbatten had been given a mandate by the British parliament to transfer the power by June 30, 1948. He advanced it to 15th August, 1947 because it honoured the second anniversary of Japan's surrender to the Allied forces.
Hindi was adopted as the official language of the Union of India on September 14, 1949. In 1950, the Constitution of India declared Hindi in the Devanagari script as the Official language of India.
The Indian Independence Bill gave August 15 as the date of independence for both India and Pakistan. Mountbatten chose August 14 as the date of the ceremony of power transfer to Pakistan because he wanted to attend the ceremonies in both the countries. Perhaps because of this, Pakistan started celebrating its independence day on August 14.
The first unofficial flag of India was hoisted on August 7, 1906 at Parsee Bagan Square in Calcutta (now Kolkata). It comprised three horizontal strips of red, yellow and green, with Vande Mataram written in the middle.
Vande Mataram, India’s national song, was composed by Bankim Chandra Chatterjee and was part of his novel Anandamath (1882). On January 24, 1950, it was adopted as India's national song.