plant's reactor/s Nos. 1, 2 and 3

The second. Three is more than one, so I would use the plural 'reactors'.

2. You could just say "The plant's reactors 1, 2, and 3...." and I'm not clear why you capitalized "Nos."

There seems to be a growing tendency in the U.S. to capitalize abbreviations, and even nouns if they seem important. We should continue to resist this innovation.

I agree, but if "No.1 Reactor" was the official name of the facility then at least in BrE there would be a capital N and a capital R, like for example

No. 1 Ladies' Detective Agency

Several bomb hits wrecked the forecastle from side to side forward of No. 1 turret

Well, yes. Actually, I used the abbreviation for United States to kind of make the same point.

That's why we put the number of an item after the noun.

Several bomb hits wrecked the forecastle from side to side forward of Turret 1.

There was a fire in Reactor 1.
Both Reactors 2 and 3 were offline when Reactor 4 blew up.

No need for either the word 'number' or its abbreviation.

Joe(Next!) Nation

Not sure what you are trying to say here, Joe Nation. If the Royal or US Navy called a certain part of a warship "No. 1 Turret", and used that nomenclature on plans and organisation charts etc, who the hell are you to say they should have called it "Turret 1"? Just asking.