The existence of a "no first use" policy in India means that Pakistan will avoid engaging in it's "first strike" policy unless it was certain that India was willing to violate "no first use." For Pakistan, there is no political upside to initiating a nuke strike when there is no exigent threat - EVERYONE would turn against them, and it's unlikely that the first strike would remove India's ability to retalliate. India knows this. That's why they created the policy in the first place.
There would have to be some horrific circumstances for India to drop the no first use policy. Even if the threat of war extended farther than just the border conflict directly into undisputed territory, it would be more strategically sound for India to let Pakistan extend itself and then surround the invading force rather than escalate the conflict. India would need to be threatened with wide-spread destruction (or a threat of complete takeover, which Pakistan isn't big enough to handle) for them to reach for the nuclear option, which the majority of the world would certainly support.
Knowing that, it would be insanity for Pakistan to attempt a full takeover of India in order to justify a pre-emptive nuclear strike AGAINST THE COUNTRY THEY'RE INVADING which would certainly doom everyone on BOTH sides.
A far more probable tactic is, unsurprisingly, the one ("not") being used by Russia (and most likely learned from it's history of sponsorship of militants) - war by proxy.
Basically, one side or another would sponsor "separatists" from the opposition to inspire local conflict to which they would provide material support. As you noted, China and Russia would be fine with this (more market for their weapons!), the rest of the world would be unhappy with the escalated aggression, but wouldn't actually DO anything for fear of further escalation (see: Ukraine). It's an "open secret" that the separatists/terrorists are directly sponsored by the enemy country. Eventually, one of two things will happen:
- While attempting to press their advantage, the sponsored terrorists will go too far.
- The defending country gets tired of world inaction, snaps, and launches an all-out assault on the sponsoring country.
This would coerce the world into broader military intervention. Whichever country is indirectly sponsoring the terrorists would fall out on their side, "arguing for mediation and localized conflict." If this works, it will probably will end up with the creation of an "independent state" under de facto control of the sponsor, effectively winning the war for them. If not, then they would send in material ground support.
The US and EU would probably end up on the side of the defenders, at the very least to put themselves in opposition against China and Russia. Any deployment of troops by them would be countered by US forces for the other side. We would end up in a "Warm War," not yet a full hotzone, and more actual military action than the Cold War.
The tipping point would come when the sponsored separatists/terrorists get ahold of a mini-nuke. Where it will come from is irrelevant. It might have been from a previously uninvolved country (such as Iran) trying to "stir the pot." With all the major world powers focused on the India/Pakistani border, a nuclear explosion at a military base containing foreign forces would throw everything into terrible, terrible conflict.
And here's why that's frightening: nuclear weapons, once used, broaden the field of war. The first use of nukes gives a "pass" to a retalliatory strike. And in this case, the retalliation will be against PEOPLE WHO DIDN'T EVEN USE OR SUPPLY THE NUKES, but no one at that point will believe them.
Why this is plausible: It could even be done intentionally by, say, a nuclear Iran (or any other middle eastern nuclear power) in hopes that the larger powers would rip each other apart, basically initiating their own eschatology via nuclear war!
Basically, the Far East will erupt into a war between all world powers, with the most of the middle east snickering at the side, glad to be left out of it this time.
In conclusion, I'll just leave this here: