What are the hindrances for India to sign 'Nuclear Non-Proliferation Treaty` and how Indian politics is working for/against it?
Because India has territorial disputes with China and Pakistan which are both nuclear powers.
Signing the nuclear non-proliferation treaty would bar India from getting nuclear weapons themselves. It would put India into a quite precarious situation when Pakistan and China have nuclear weapons and India can not. India would then no longer have the option to threaten or execute any military actions because they would have to fear nuclear retaliation. The only way to keep an enemy state with nuclear strike capabilities at bay is to have enough own nuclear strike capacity for mutually assured destruction.
India might be able to negotiate a deal to sign the treaty in exchange for some western partners stationing some of their nuclear arsenal in India with the promise to use it to retaliate against any 3rd party (the same deal some European countries got in the cold war), but that would be a quite unreliable agreement and would mean more permanent military presence of other countries in India. So having an own nuclear arsenal is far more preferable.
Also, there is not much to gain for India from signing the treaty. The usual deal is to offer a signatory support with building nuclear power plants for civil use. But India's nuclear power industry is already well under way and already got plenty of support from abroad, so there is really no need to sign the treaty.
The main hinderance is that the treaty effectively divides the world into two camps; nations who can be trusted with nuclear weapons and nations who can't. I personally disagree with the notion.
Signing the treaty could be interpreted as a permanent acceptance of subservience to nations who already have nuclear weapons, so development of nuclear weapons by a nation could simply be out of a desire to obtain parity.
Despite the claims made by Tony Blair at the time, it is unlikely that the UK would have invaded Iraq if it was truely believed to have nuclear capability - and judging from the current instability in the region, a nuclear Iraq might have resulted in a more stable world, or it might have resulted in nuclear war.