The russian organization of their military was somewhat similar to their central european counterparts. The rich landowners and noblemen would recruit large infantry masses from their cities and lands. These infantry masses were lightly armoured and used whatever weapons they could get their hands on. Their strength were their numbers and if they were well disciplined and somewhat organized they could be a potent weapon.

The noblemen and rich landlords themselves served as heavy cavalry together with their followership. These armoured horsemen were the "druzhina" you mentioned. Their role was similar to european knights and they were the crucial element of the army.

Overall the infantry and cavalry had to work together in order to guaranter success. They were organized in "polki" which are just large regiments. Usually 5 of these were created. The advance guard (peredowoi polk), the big regiment which stood in the centre (bolschoi polk), the right wing (polk prawoi ruki), the left wing (polk lewoi ruki) and a rear guard. These regiments would be screened by cavalry which also took up the task of scouting. The advance and rear guard, as well as the scouting force, were usually pure cavalry. The other 3 regiments were a mix of infantry/cavalry. These regiments were commanded by noblemen with military experience. Overall the russian armies were similar to their european counterparts, but they had a larger focus on infantry.

Please note that these things are mainly applicable to 13th/14th century russia/the moscowvite kingdom. Things may have looked different in the early 12th century.

Schnitter, H. Von salamis bis diem bien phu, berlin, 1987

Rus' armies of 12th-13th period were both similar and dissimilar both to their western and eastern neighbours and were, from a certain point of view, some kind of mix between the two.

To understand how Rus' forces of this period were organized one must understand geography, politics and history of the region. Regions surrounding Kievan Rus were vast and relatively sparcely populated in comparison to much more close knit western European kingdoms, and its southern and eastern borders were under constant threat from different nomadic peoples. Essentially, entirety of Rus history from early Medieval to Renessaince is a history of confrontation between Rus' (and, later, Moscow State which would transform into modern Russia proper) and Pechenegs, Cumans, Mongols and Tatars. Simultaneously, being scattered across vast territories, Rus principalities often warred with each other, and some (Galich Principality, Novgorod, Pskov) - just as often with western countries, such as Poland, Hungary, Lithuania and Sweden. This obviously led to different manners of force organization in different principalities, but some things were more or less the same.

First of all, knyaz (or prince) was de jure military leader of his knyazhestvo (principality). Boyars, or principality's ruling noble elite, were his subordinates, but it wasn't uncommon for boyars to directly oppose their prince since they were very powerful figures and could theoretically either expel their prince or make him give substantial concessions. Many times boyars were in opposition to their ruler for obvious reasons: they were powerful feudals and, like any other proper feudal of this epoch, didn't like to follow orders of their king, especially if said orders were harmful to their freedoms or finances. Boyars ruled fiefdoms throughout the principality and also maintained highest posts in principality's administration and were also responsible for providing equipment and funds necessary to maintain principality's armed forces.

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At this time, did the word "druzhina" mean the entirety of the army, or only an elevated portion of it?

Druzhina is a term reserved for noblemen under direct command of their knyaz, essentially they were Russian knights. Druzhina was usually divided into two parts: older druzhina and lesser druzhina. The first one consisted of Boyars and their closest retinues, the second one was usually comprised of lesser noble houses and elevated commonfolk. Druzhina in its entirety almost always comprised out of mounted warriors, both heavily armed lancers and lightly armed horse archers.

The rest of the army was composed of "chernie lyudi" (literally "black people", or "commonfolk") - these were militiamen or assistants, such as non-combat retinue, cooks, guides et cetera. Rus' militia was usually few in numbers and richest cities (such as Novgorod) also tried to provide horses for them, although obviously unarmoured and of lesser quality - having a lot of infantry considering distances between population centers and active presence of nomadic horsemen didn't make much sense. Infantry (or "peshzi"), however, was still present. Its main role was in sieges and city fights where cavalry masses were obviously quite useless (until the walls were breached, at least). Sieges were usually conducted by sniping out defenders with arrows and taking the walls in hand to hand combat or by starving opponents out since medieval Rus' rarely used siege weaponry such as catapults. In addition to that, infantry was key component in organization of naval forces (sudovaya rat') for sea raids. Masses of militia infantry were a rare sight on the battlefield and usually didn't bring much to the table in terms of effeciency (for example, they were quickly put to complete rout and annihilated during battle of Lipiza, 1216)

In addition to their own horse archers, Rus' princes actively employed their nomadic vassals called chernie klobuki (literally "black hats"). These nomads would often provide sizable chunks of princes' forces and would sometimes hold important positions, such as military advisors.

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the formation of the Boyar social class and the Boyar Scion social class.

I suppose by Boyar Scion you mean Boyarskie Deti ("Boyar's children)"? These were at first synonymous with members of lesser druzhina (although the term Boyar Scion would only start to appear in late 13th century and wouldn't gain prominence until 15th) and would transfrom into the most numerous noble class of Russia much later, in late 15th century.

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Much of the history of Kievan Rus seems to be tied with mercenaries, would mercenaries still have been employed at this time?

Mercenaries such as nomads, Hungarians or Germans were indeed employed by Rus' princes, but they were usually innumerous, distinct and didn't serve for prolonged periods of time, thus their influence on Rus' military affairs wasn't really very big. Proper use of big amounts of Western mercenaries starts in 16th century Russian Tsardom, which is out of scope of medieval period.

I hope that clears things a bit.