Yes, there are some hints of a special bond between Chhota Bheem and Chutki in the series. Their relationship is more of a deep friendship which can be seen as a precursor to a love story in a very innocent way. They are always there for each other, through all the adventures in Dholakpur.
In the Jungle Book Mowgli story, Mowgli's main adventures include his struggle against the evil Shere Khan. Shere Khan wants to kill Mowgli because he is a human. Mowgli, with the help of his animal friends, tries to outwit the tiger. He also has adventures in learning the jungle's secrets. He learns how to climb trees like a monkey, swim like a fish in the jungle rivers, and hunt small prey. His relationships with the other jungle animals, whether friendly like with Bagheera and Baloo or hostile like with Shere Khan, form the core of his adventures.
It depends on how you define 'true'. Some parts might be based on real events or inspired by them, but it likely has fictional elements added for dramatic effect.
It can be considered a real story to some extent. Maybe it takes inspiration from actual incidents and then adds some fictional elements for dramatic effect.
Yes, 'The Jungle Book' which features Mowgli has some elements based on real - life in India. Rudyard Kipling, the author, was inspired by the jungles of India and the various animals and cultures there. Mowgli, the boy raised by wolves, represents a fictionalized version of the relationship between humans and nature in that context.