Don't go for it. Rahul Gandhi is too unpopular, and there are even whispers of scandals during his pre politics days. Moreover, there are many hidden skeletons in the Gandhi familiy's closet. I suggest working with an OC if you want a post 1990 SI, since it will give you more freedom to develop a specific background.

There were historical, cultural and practical reasons for keeping the capital in delhi. Since the times of the Mahabharata, Delhi has been the Indian capital at various points of time. Delhi being a small state, there may be a small minor, if any tussle between the center and state governments. If you set up the capital in a major state like Madhya Pradesh, which will have a relatively stronger government, there may be heavy tussle between the governments. Another advantage of Delhi is that it is connected with yamuna. If you develop the national waterways, delhi will be connected to almost every state in Northern India. Another issue you raised is of invasions. I feel if the invading force manages to reach Delhi, there is something seriously wrong, and nothing will prevent them from reaching wherever you set up the capital. India gets a lot of its revenue from North if Delhi, and loosing land till there would make it even more unsuccessful than OTL Pakistan. As for Tibet, it will be overextended for the Indian forces. Himalayas serve as a natural barrier and easy to maintain. It would be better to just establish military bases and have a relation like US has with it's NATO allies. For the northeast I suggest that you keep it in India. The major problems was the lack of connectivity, which is due to OTL Bangladesh. This is not an issue in your timeline. Policies of the government of the past 10 years can be taken as a template. Except for Manipur, they have been fairly successful (enough that one of the north eastern states get a semiconductor factory, it was Assam I think) For Manipur, it was a princely state at that time as far as I remember. The issues in northeast are mainly due to the mismanagement of the congress and Nehru-Gandhi family. If that is avoided, the north east can easily be integrated. You are right for Burma. It is best to do a NATO like alliance with them. Though unlike Tibet, there is no natural barrier separating it with India, so it can be integrated with the country easier than Tibet. Though it will be tough enough for it to be not worth it. Better course would be to install friendly governments there. The middle east can be reconciled using regional rivalries like sunni -Shia. Though Egypt os relatively important due to the Suez canal, and requires extra efforts. Another country that I think you have overlooked is Panama. Quite a lot of the world's shipping goes through the Panama canal, and India having a piece of it will be a good boost.