What is the weight of a 5.56 mm bullet - say INSAS. Bullet alone - not casing/propellant
Similarly what is the weight of a 7.62 mm bullet.
Does the 7.62 Kalashnikov share ammunition with the old FN/Ishapore rifle? Does the AK 47 take 7.62 at all.
Is lead still used in the core of bullets?
Different weights can be found in bullets of the same caliber. For example the NATO-standard round is slightly (by a few grains) heavier than the US-adopted rounds. They can be inter-changed with marginal issues with performance. If the design features attributed to INSAS on the BR read-up is true, it is more heavy like the NATO standard than the US-adopted standard.
Again there is much difference between different bullets of a 7.62mm round. Also 7.62mm is not a conclusive definition of even a similar family of a round. This I shall elaborate on next point.
The Kalashnikov round is 7.62x39mm, the NATO standard is 7.62x54mm. There is no way you can fit either round into a gun-chamber designed for another. Yes, the AK very much takes the 7.62x39mm rounds... its the only round it takes in fact.
What exactly do you want to do with a bullet? If the job has particular characteristics, you will be recommended an appropriate bullet - some with lead-cores if need be. Regular military cannot use expanding bullets(which I presume is the reason you want a half-jacketed lead round?), even Special Forces are very iffy, NSG - as a quasi-police force - can use it in their arsenal quite legally.