The first two answers are... great. However, it's too bad you cannot exceed the character limit and therefore should look for a way to cut out more than half of your answers for each prompt.
So... Here are my suggestions.
My thought process has always deviated from the norm- something that isn't really appreciated in the Indian educational system.
For example, this sentence is somewhat repetitive. Without it, the message you're trying to convey will not be lost.
Although I have a good academic record, academics has never held the most important place in my life.
The adcoms will probably know you have good grades by referring to your transcript. Also, I'm a bit concerned about the part after the comma... Again, I don't think there'd be a major change in your 2nd paragraph if you remove this sentence altogether.
I have seen how hard it is to co-exist peacefully because of all the problems currently faced by the world body, but have also seen the importance to do so. Different cultures and world-perspectives greatly interest me, and I feel that my experiences and knowledge will grow, if given an opportunity to attend Brown, making me better equipped for my possible future in politics of international relations.
Hmm... sounds quite generic. Besides, these sentences don't deal with why and how your experiences at MUN helped you to develop communication and diplomacy skills.
Oh, btw, since you are going to talk about MUN mainly for the second prompt, maybe it's not such a good idea to write about it twice.
Moving on,
Although an extremely difficult task, some day I definitely want to play a role in the restructuring of the Indian judiciary.
and
I definitely want to make a positive impact on the world, something I will be able to do by being a part of the judicial or political system of a developing country like India.
Some parts of these two sentences overlap. Plus, "I definitely... world" part is generic.
Among other things that I don't know- I am not yet sure of what I want to do after I graduate - but I do
know that it has to make a positive difference to our world.
This last sentence from your answer to the last promt contradicts your statements you had made in your answer for the 2nd prompt. Didn't you mention that you want to become a diplomat?
Lastly, try to avoid using phrases like "I feel, definitely(as in "I definitely want to...", etc.
Okay... I hope this helps.