To answer your first question you have understand the depth of polarisation and, yes, class tension that existed in Russian cities before the February revolution. There had long been a social cleft in urban Russia between the demokratiia (lower orders) and tsenzovoe obshchestvo (propertied classes). Crucially, the social struggle between the two had given rise to very different political traditions. The Duma was ridiculously stacked to favour conservatives and, in turn, a strong socialist and anti-capitalist subculture developed in working class Russia.

So when the Tsardom collapsed in Feb 1917 it left a vacuum into which stepped two very different traditions. The Provisional Government inherited the old state bureaucracy and drew its legitimacy, however removed, from the Duma. The Petrograd Soviet in turn resurrected the traditions of 1905 and, importantly, was directly elected as a class organ.

In 1917 the popular classes in urban Russia had a choice between a removed Provisional Government of princes and notables and a soviet, an institution that in theory belonged to them and advocated in their interests. At last the demokratiia had its own organ of power. The problem for the Provisional Government is that it was always seen in the same light - as a class body that represented the elite, rather than an inclusive national parliament.

(Ironically, these deep divisions were briefly healed by the February Revolution. A 'fashion for socialism' became popular amongst the propertied classes and there was strong Soviet backing for Provisional Government. This began to unravel quickly though, to the Bolsheviks' advantage.)

The above also feeds into your second question. These traditions of self-governance (from 1905) and the distrust of all previous formers of authority led to an explosion of elected bodies throughout Russian cities and armies. Revolutionary councils mushroomed across the country in a fairly uncoordinated manner as workers and soldiers sought to 'defend' the revolution by limiting or usurping the power of the suspicious former elites and bureaucrats. There was little direction to this initial spread: there were probably 400 in May, 600 in August and 900 by October. And this was in addition to soldier assemblies, factory committees, unions, etc.

So how did the soviets coordinate? In large part they didn't. In theory there was a rough pyramid structure - from district soviets all the way to All-Russian soviet - but that never really took hold in 1917. Instead the key links were forged at regular All-Russian Congresses of Soviets, of which there two in 1917 (June and October). Each of these drew about a thousand delegates from various soviets to Petrograd to elect a Central Executive Committee (CEC) which was in theory the apex of the Soviet movement.

In practice, none of this was clearly defined. The CEC tended to compete with the Petrograd Soviet which, as a product of its revolutionary pedigree (in 1905 and 1917), remained the lodestone for the national movement. Decisions would be made in Petrograd and rather communicated across the country in a rather ad hoc manner. These were chaotic days.

(The same applies to most institutions in 1917. We tend to use the terms 'soviets', 'unions', 'ministries', etc as shorthand but for most of the country this was a period of feverish change. Institutions were being torn down or erected and there was little the centre could do to impose uniformity. Conditions varied massively across the country so keep in mind just how chaotic things were.)

Sources:

The first half is fairly general and you're in good hands with Suny. For more specific works on working class attitudes I'd recommend Smith's Red Petrograd and Kaiser et al in The Workers' Revolution in Russia 1917. Both are very much views 'from below'. Kolonitskii's essay *Anti-Bourgeois Propaganda and Anti-*Burzhui Consciousness in 1917 is also worth a read.

For the soviets themselves, Anweiler's The Soviets is pretty old but probably still the best monograph on their development and relationships with other worker organs. Has less to say about what the workers themselves thought though.