Unclear. Current evidence is that nukes are insufficient, and given the non-trivial chance that the next U.S. administration would pull out of NATO, it’s not even obvious that the nukes would be a factor.
Someone else’s nukes being insufficient. The last few years have shown nuclear powers are inviolable, to the point of causing allies of non-nuclear powers being violated by them drawing red lines in the violator’s defence.
No. If we only had nukes, Russia would have little to fear from invading neighboring countries with conventional weapons. Have our nukes stopped them from doing so now?