Not very well. Although tightly centralized in Russia proper, until at least the 19th century or even the early twentieth, the reach of the Czar in Siberia was mostly indirect, barring the very occasional regular military expedition.
Siberia was of much less political interest than Europe and thus was neglected.
Yes, but these trading post/forts were mostly quasi-autonomous.
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When Russian soldiers came across some Asiatic Siberian tribe, to what degree did these folks consider themselves Russian?
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Generally not at all - they were sullen subjects at best, actively hostile at worst.
Yes, the yasak. In of itself it was not seen as unnatural by the Siberian tribes, who were used to being taxed in the same way by their more formidable cousins on the steppe to the south. The problem was that the local Russian/Cossack warlords ( Telly Savalas plays a jim-dandy one as Captain Kazan in Horror Express, which despite the lurid title is a surprisingly decent little horror/sf movie set on the trans-Siberian railway ) were greedy, extortionate thugs that tended to tax to the point of provoking local rebellion. Moscow attempted to stem this ( which resulted in valuable subjects fleeing across the borders into Dzungaria or Manchu China ) by setting standardized tax rates, but local authorities eeled around it by demanding “gifts” on top of the yasak.
Pretty much, yes. Of course by locals, I mean local Russian voevodes. The tribes might have some internal autonomy, but they were conquered dependents on local Russian commanders.
Nothing. Warlordism was not just the rule, but near-universal until political exigencies ( compeition with China, the Great Game with Britain ) forced the extension of central authority late in the game.
Generally what happened is minor official/warlord clashes with neighboring tribe, either after being raided, horning in on fur grounds, whatever. Conquers tribal neighbor with their advantage in firearms and sets up new outpost/fort further east to oversee and tax new territory. Which brings him in conflict with next set of neighboring tribes and so on until they hit the Pacific ( and beyond ).
To quote:
From approximately 1550 to 1800 these several foreign policy issues preoccupied the attention of the Tsars. During these years the relations of Russia with Europe and the Ottoman Turks became the top consideration, while Muscovite relations with other parts of Asia such as China or Mogul India were definitely of secondary importance. Moscow had the same attituide of neglect towards the conquest of Siberia. The Russian Tsar in Moscow, despite all the centralizing tendencies of his burecracy, left the chief work of the administration and defense of Siberia to his local officials or voevodas. These provincial functionaries and private persons of the settlements first founded and then enlarged Russia’s empire in Siberia. They repeatedly operated on their own, procuring the approval of Moscow for their activities only after they had already accomplished their objectives, not bothering to seek Moscow’s permission beforehand. No one in the center of Moscow at Moscow seemed to have the time to sit down and work out a detailed for Ruissian expansion in northern Asia. They did not trouble to scrutinize closely and regulate events in Siberia. The local voevodas, who governed the districts in Siberia with their Cossack servants, pursued their own course for the most part, with only an occasional decree coming from Moscow moderating their behavior. In making policy decisions, three basic motives ruled the voevodas’ operations; a. the need of security from outside attack for their bailiwicks, b. the the prestige of empire building, and c. the love of adventure of their Cossack subordinates.
From The Partition of the Steppes: The Struggle of the Russians, Manchus, and the Zunghar Mongols for Empire in Central Asia, 1619-1758 - A Study in Power Politics by Fred W. Bergholz ( 1993, Peter Lang Publishing, Inc. ).