This Cold Start doctrine is highly questionable. It is all too dependent on Pakistan reacting in a certain manner to IAs 5-70 km incursions into Pakistani territory. What if Pak military reacts differently and immediately goes nuclear? Yes, in the end India might outshoot Pakistan in a nuclear shootout but at a very high cost to India.
What India should be developing and learning is Israeli style (or a some extent American style) covert actions against external threats. India should be strengthening its external security agency to the level of the Mossad, CIA and their Special Forces (a military force on its own uninhibited by laws of war). An formidable ability to do tit-for-tat unconventional action and to disable key enemy infrastructure deep within enemy territory (with full deniability). The Cold Start and the IA conventional forces should be there simply to deter an all-out Pakistani response to covert actions (I think nuclear weapons can do a better job here)...
Simplistically put, in any campaign/ battle, the advance is not on one single front. If it were so, then the adversary would be able to position his mobile/ blocking forces along that line of advance and the whole campaign would become a slugfest with no tangible result.
The crux of any battle is what is known as 'reserve management' wherein whether in defence or attack, the reserves are positioned to change the 'combat ratio' wherein the adversary's plan is brought to nought because, at the critical moment by moving in the reserves, the strength becomes too much to overwhelm.
Therefore, when attacking, since the attacker has the initiative, he moves on a multiple thrust line, they being the Main (which is what will change the complexion of battle), but at the same time to fool the adversary and make him commit his reserves prematurely or incorrect, have a subsidiary thrust, and, ideally a diversionary thrust and even a feint. The cardinal principle of all these thrusts is that they must appear to be similar. If they are not similar, then the enemy is not kept guessing and thus not fooled and can judiciously position his reserves and block the main thrust.
The above would indicate that in the fog of war, which is the Main cannot be discerned at the word 'go'. It takes time since the diversionary and the feint would peter out and will allow the enemy to have some idea where the real action is going on. This time lapse, as a thumb rule, could be between 48 to 72 hours.
Therefore, it would be safe to assume that Pakistan would not launch a nuclear war immediately after the Indian forces commence the Cold Start or whatever it is called.
The rest of your suggestions are valuable.