The most common nuclear attack scenario was one which followed a brief period of international turmoil, and began a general offensive in Europe. So, to answer your first question: Nobody really cared about a declaration of war.

First we need to constrain our period a bit. By the late 1950s, both the US and USSR had developed rudimentary ICBMs. While there wernt many of them, and they wernt terribly accurate, they existed and they could drop a nuke on a city halfway around the world with little-to-no warning. Prior to that period, nuclear war was dominated by the bomber. Following that period, it was dominated by the ICBM.

So in the era prior to the ICBM, bomber based bombing was tricky. The USSR is pretty big, and even the closest American bases are pretty far away from key targets in the USSR. So after the go-code was issued (regardless of the reasons why it was issued) it would take hours for the first wave to hit their targets. And follow on waves could take days, weeks, or even months before they could relocate to suitable bases to launch more attacks, especially if bases were destroyed in the first attack. While nuclear war could be just as destructive, there was a slower pace to fighting nuclear war, a pace dictated by the speed in which bombers could be tasked and retasked to drop nukes on their strategic targets.

But the bomber solution creates a whole headache of other issues. ICBMs, on the other hand, skirt many issue because they launch nukes into low Earth orbit, then deorbit them over their targets. These warheads then come hurtling down on top of their targets, and detonate in spectacular explosion. The most relevant advantage to that system is speed. By the 1970s, ICBMs could hit their targets within 60 min of launch, and could hit anywhere in the world. Sub launched ballistic missiles, fired from the nearest sea, could land inside 20 min. The rapidity of that threat completely changed the way both superpowers conceived of nuclear war, and planned to respond to nuclear war.

So, to your first question again: In the bomber days, the process from peace to nuclear exchange was a bit "slower" in that it could take hours or days for the enemy to organize their forces and attack. All sorts of things could be done in that period. A retaliatory or preemptive strike could be planned, a ground offensive could kick off, smart diplomacy might prevent a conflict, etc. It gave politicians a brief time to react and decide how the conflict should evolve.

But with the ICBM, planning had to happen at a lightning pace. Before the advent of satellites which could instantaneously relay a possible launch to CnC facilities, RADAR might only pick an ICBM up after it had gained some altitude. And SLBMs could strike almost without warning. All that meant that there was zero time to deliberate or consider the niceties of the situation. Once an attack was confirmed, there was only one possible choice: to strike back.

As for targets, that again varied widely from period to period. Generally, until the 1980s nukes were fairly inaccurate. Bombs werent perfectly accurate, and early ICBMs could be over 1 kilometer off target. All that meant that bombs had to be big (which, for bombers meant that they had to drop at an even higher altitude, and thus risk an even less accurate drop), and they had to target big things. Realistically, cities were the only viable target for strategic level bombs. Further, the existing doctrine for nuclear war argued that targets should be selected which would paralyze a nations ability to respond militarily. So, military outposts, bomber bases, sub pens, and missile silos were generally high up on the target list. So was political centers and capitals, where a response could be coordinated. And so were industrial centers, where new weapons could be manufactured.

Now, army bases actually tend to be dispersed in rural areas and built on large tracts of land, especially when those bases house atomic weaponry and state secrets. But a nations political infrastructure is innately tied to the people it governs. Think of the political value of Washington, LA, New York, and every state capital in the US. Politics needs people, and where there are a lot of people, the political apparatus is strong and important. And industry too needs employees. Big industries need lots of employees. So they too tend to congregate in the largest urban areas.

So the act of attacking these targets of perceived military value tend to also target the civilian population, who happen to be collocated with those targets. The civilians were never the target, per say, but they were definitely in the line of fire. And there wasnt much way around it. Nuclear bombs are big weapons, which do a lot of destruction. They are wasted on forest, mountains, deserts, or places where there isnt anything to destroy. And thats what makes nuclear war so scary. The outcome of nuclear war is the destruction of every major city in the US and Europe, the destruction of western culture. Nearly every city has some value as a rail hub, a communications center, a political mecca, or an industrial base. Humans tend to make those large networks wherever we get together, and theyre the best targets for nuclear war. They go hand in hand, the destruction of civilian and military targets. And even if we ignore the vast destruction of the explosions themselves, the fallout from such a large exchange would surely kill anybody who survived.

I would argue that in light of that reality, many of the rules of warfare and civilization end. Planners didnt care about things such as "declarations of war" or "civilian casualties" because they just couldnt be factored into any reasonable scenarios. There was no time, and no realistic avoiding, violating those rules of civilized conflict.

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Sources

Lawrence Freedman's The Evolution of Nuclear Strategy

Robert Aldrige's First Strike!