That is incorrect. NATO policy is "no-first use" for nuclear weapons. The member countries individually can make decision. Nothing in NATO mandates use of nuclear weapons, just that they join in common defense.

I think you misunderstood. "Initiating MAD" doesn't mean launching an attack. It means assuring that any full nuclear attack is met with a similar counter attack, ie. the "Mutual" part of "Assured Destruction". If you don't respond... there's no MAD.

Do you really think that the US will nuke Russia to protect Poland or Germany?

Germany is virtually the sole power keeping the EU from collapsing on itself economically geographically and politically, even if France is the one with the nuclear arsenal.

The US has thousands of US soldiers in EU NATO states, do you think US will just sit there and talk about financial sanctions while Putin kills US troops in Europe?

By the way Germany also has nukes, not their own ones, but they are not just there for fun.

While there are nukes in Germany, they're not Germany's nukes unless Germany can determine when/where said nukes are used. (The ability to stop the US from using them is not enough.)

If Russia uses nuclear weapons first in a European war then yes. But the targets would probably be Russian forces in or approaching Poland or Germany rather than mainland Russia itself.