Well they began considering it because they didn't want another armed revolt like the Americas did. So they peacefully let them leave. Also they let them leave so they could be allies and be valuable trading partners. Also they knew they had enough to deal with like the threat of the cold war bombing. Plus they didn't want India turning to Soviet communism influence. This a basic summary of why they peacefully seceded India and let them become their own country.
Answer:
I think that the conclusion that I can draw in regards to him helping Hilary is that he endorsed her. The words of a former US President would likely make Hilary look really good in the limelight. Which is what happened. Since Obama was fond of her and publicly endorsed her, people thought she'd be a good choice in terms of Obama's judgement.