Highly doubtful. Ya it will possibly escalate but both nations are big enough and well armed enough to battle it out between themselves without other countries getting involved.
Maybe... but other countries don't need to get involved. The two countries have enough nukes for a global nuclear winter even all blasts are contained in their territory. If you can last a decade on your reserves (energy to filter air, provide light to grow food, etc.) you'll be ok. 99% of us will starve and leave behind a pre-industrial society.
I've been predicting these water conflicts for a 1.5 decades, and I'm happy to see it's been getting attention the last couple years. In the US they fight using laws; in South Asia they fighting using weapons. Sticks and stones so far, but if your armed forces are about to collapse from lack of water, are you just going to surrender with "ok, you win. I'll let my hundreds of millions of citizens die"?
I don't think they have very powerful nuclear weapons to damage so much rest of the world.
But yes nuclear might be case with them i guess Pakistan strike