Lots of interesting questions! I think we should distinguish the Far East from Central Asia (and even this is quite a broad brush), but that may help us tackle the process of colonizing Asia. Siberia was conquered in the 16th and 17th centuries by both state and private actions (due to the fur trade; the city of Tyumen was established by cossacks with the support of Fyodor to collect both taxes and furs from Siberia), and by the 18th century had effectively controlled it; Yelisaveta Petrovna, the constructor of the Winter Palace for example, is widely recognized for not executing a single Russian subject - but oversaw the near-genocide of the Chukchis before brokering a rather tenuous 'peace'.

The conquest of central Asia does not take place until the 19th century, and even bleeds into the 20th; earlier Russian presences were certainly there, but were unstable. Nur-Sultan (Akmoly) is an example of an early Cossack settlement. The invasion of central Asia was a state project enacted to expand the Empire for a multitude of reasons, one of the more intriguing being the British Empire's presence in southwest Asia (e.g., the Panjdeh incident) and by the 1860s the Russian Empire had taken to Central Asia to increase cotton production (highlighting just how globalized the mid-19th century world was, this can be read in part as a response to American declines in cotton production due to the American Civil War). And this a rather fraught endeavor; several key Russian *losses* include the early invasion of the Khivan Khanate as well as several significant losses with the Emirate of Bukhara, only by the late 1860s becoming a vassal state.

The state does enact internal relocation policies, especially for the conquered peoples, and central Asia certainly had quite substantial cities, including Samarkand and Tashkent.

/u/kochevnik81 has written on Central Asia in great depth which should be a great resource!