Unless the nuclear war is propagated a lot more in the media, I don't believe most Germans will take it seriously... for now. We currently have no nuclear weapons so from my perspective it's out of our hands anyway. Just because Putin mentioned it doesn't mean Germans see it as realistic. I can obviously only speak for myself but noone in my surrounding has mentioned it as anything more than political leverage.
Regarding sewing discord between western allies: The nordstream pipeline has been a point of contention between western allies and quite controversal in inner german politics. I don't see that changing, if/when the pipeline is used there will be outcries from allies and within Germany. Economically the choice might be made anyway because the energy prices in Germany are just extremely high and not all gas usage can be replaced by other sources.
Regarding refugees, it's hard for me to estimate the impact. This is honestly something i feel i should research a bit. My opinion is that short term such changes in population can have unforseen effects. Long term I believe it helps Germany with it's declining population. All the arguments regarding culture etc. don't mean much to me personally as all that changes over time anyway and clinging to some notion of culture tied to a geographic location is presumptuous. If you want a certain culture in your life.. then live that way.