If you don't mind I will answer this question, and Maduri can answer it as well. (I had a thread very similar to this in the past: "Hinduism: Ask your questions")
How old is Hinduism? Hinduism is approx 10,000 years old going back to the Indus valley culture. The dating of the Vedas by astronomical, geological and archaeological data place the Vedas around 7000 to 8000BCE. However, even if we do not accept this date and go with the rather arbitrary date of 1500BCE assigned by early indologists, the various traditions of Hinduism are still continuous with the Indus valley civilization. It is fair to say Hinduism is the oldest living religion in the world.
Who wrote Bhagvad Gita? According to traditional and religious dating the Bhagvad Gita was a part of the Mahabharata, and was dictated by the eternal Ved Vyasa and transcribed by the god Ganesha. This is obviously mythological, the scholarly consensus is that the Gita was written by some anonymous authors, from perhaps the early Vaishnavist tradition and then inserted into the Mahabharata.
The religion of Hinduism is divided because it is a 10,000 year old tradition and over 10,000 years it has fragmented into thousands and thousands of sects. It is also due to the fact that Hinduism celebrates diversity, and this attitude can be found in the Vedas itself, "The wise call the one, by many names, they call it Indra, Mitra, Varuna etc" The Vedic religion developed this philosophy of the one existing as innumerable manifestations. Then in the Upanishads the idea of Brahman was formulated as both transcendental and immanent, leading to the notion that all was Brahman, trees were Brahman, sun was Brahman, sky was Brahman, there was nothing that was not Brahman. This is why Hindus worship pretty much everything from rivers, trees to mountains, and even animals.
One of the concepts to emerge from the Upanishads was also the idea that Brahman sustains, preserves and destroys the universe, this was later formulated in post-Upanishadic times as the dogma as Trimuti(Brahman, Vishnu and Shiva) and this lead to the various sects, those that worshiped Brahma, those that worshiped Vishnu and those that worshiped Shiva, and later sects formed that worshiped the divine mother(although goddess worship maybe traced as far as back as the Indus Valley period)
Why is Brahma not worshiped? According to traditional dogma Brahman is not worshiped because Brahma was cursed or became arrogant, or something like this. The actual truth is probably because the sects of Brahma did not take off, in the same way the sects of Vaishnavism and Shiavism did. Vaishnavism was the most powerful sect, forming into a religious like tradition very similar to Christianity, with Krishna as their beloved saviour. The worship of Krishna was very strong among the Indian people, and because of the Gita Krishna became very famous and was treated like god-incarnate. Unlike Jesus, the character Krishna in the Gita claims to be THE God.
Shiviaism took off, because Shivaism is one the oldest religious traditions of India, going back to the Indus times. It has been more prevalent in South India.
PS Hope you don't mind Madhuri