That's entirely outside of NATO's purview and charter, so it's a fantasy not even worth exploring. The only no-fly zone NATO will ever attempt to enforce will be over NATO countries - which is just as it should be.
Um, no, the other No-Fly Zone is the future No-Fly Zone the US intends to establish when it gains control of the eastern Russian republics.
That's why Ukraine is important.
Russia wants a neutral Ukraine as a buffer-State between NATO and Russia, just as Belarus serves as a buffer-State between NATO and Russia.
If you don't understand buffer-States, then you don't know your history, and you especially don't understand Russian history.
Ukraine is even more important now that Russia controls Crimea.
Russian surface groups can operate out of Crimea and they're extremely good at providing anti-ship/anti-air screening. They would shoot down US/NATO aircraft coming out of Romania, Bulgaria and Turkey to enforce the future No-Fly Zone. Russian ADA systems in Crimea will also help.
Then there's the matter of using Crimea as FOBs for Russian fighters to interdict US/NATO aircraft and Russian bombers to destroy US/NATO airbases in Romania, Bulgaria and Turkey attempting to enforce the future No-Fly Zone.
If NATO intervened in Ukraine, I do not believe that would directly trigger a nuclear exchange. Such a conflict would be, ultimately, yet another in a long line of proxy wars that resulted in great harm and damage to many, but no nuclear detonations. What it would do, unfortunately, is put NATO forces potentially within miles of Russian territory, and a conflict that spills into Russian soil may well create the pretext for a nuclear exchange.
No, it wouldn't.
The US ERWs (Enhanced Radiation Warheads) or "neutron bomb" if you prefer were removed from the Army inventory and dismantled by 1993.
Russia still has ~3,000 ERWs ranging from 1 kt to 12 kt (20 kt is the limit).
Those are tube fired artillery in the 1 kt range, plus short range missiles in the 5 kt to 12 kt range and gravity bombs in the 5 kt to 12 kt range (and possibly the 1 kt range, too.)
The good thing about neutron weapons is that US troops will have up to 3 days to contact their families before they keel over and die
You're missing the point.
Do you think a person, who would launch nuclear weapons at us if we intervene militarily to stop his invasion of Ukraine, would hesitate to invade little old Latvia (another former Soviet republic) simply because it's a NATO member?
No, you're missing the point.
Russia is not interested in expansion. Russia is only interested in neutral buffer-States between it and NATO.
I think a nuclear war is a very unlikely possibility. Putin grew up during the cold war. He understands MAD quite well. He doesn't want to rule over a smoking crater.
He wouldn't be ruling over a "smoking crater" but then you'd never know since you and 300+ Million Americans will be dead in less than 6 months, and only 2 or 3 450-750 kt warheads detonated 85 miles above the surface would be needed to do that.
The biggest concern is that there's something wrong with Putin and he's no longer capable of making rational decisions. If that's the case, then a nuclear war becomes a bigger possibility, but I still think it's still fairly unlikely. I think he'll get deposed first.
Invading Ukraine is a rational decision.
The US wants the eastern Russian republics. This is just King's Knight to King Bishop-3.