Short Answer: Yes, Nicholas II was well aware of radical movements in Russia and Europe. The historians Catherine Evtuhov and Richard Stites characterize his government as playing a "cat-and-mouse game...[with] the "progressive" elements of society" (Evtuhov and Stites,190). The Tver Address of 1894 explicitly rebukes local liberalizing governors as harboring “senseless dreams” (Esthus), and all throughout his reign Nicholas dealt with protests, strikes, and revolutions.
But understanding the political scene under Nicholas II requires stretching back a little further.
Longer answer:
Political radicalism in Russia has Enlightenment antecedents, such as Alexander Radishchev, who was exiled to Siberia by Catherine the Great. By the late-nineteenth century, however, the intellectual landscape was incredibly fractured, so I will focus on three specific moments: the Russo-Turkish War of 1877-78, the assassination of Alexander II in 1881, and the Russo-Japanese War of 1905.
i) The Russo Turkish War. The Russo-Turkish War followed the Crimean War of 1853-56 with renewed vigor, and was reliant on a particular pan-Slavic nationalism that was absent from previous conflicts. Russia succeeded in regaining Ottoman territory, while the Balkan independence that resulted from this would be a powder keg that erupts in 1914. Bismarck oversaw the division of these states with the Treaty of Berlin, reducing the Russian benefit of the war while leading to Austro-Hungarian influence in the region.
Politically, the war gave rise to relaxed censorship. An assassination attempt on Alexander II in the mid-1860s, following the successful annexation of the Caucusus, massively restricted public radicalism, but this just pushed it underground, in more extreme circles; the nihilist and radicalism of the 1860s is probably best seen in Nikolai Chernyshevsky's What is to be done?, for which he was imprisoned, though it was distributed in the intelligentsia journal Sovremennik. The nihilist Sergei Nechayev significantly influences the Bolsheviks with his manuscript Catechism of a Revolutionary, composed in 1869 and distributed both clandestinely and abroad. But the war relaxed this censorship and brought these violent secret societies into wider view. Anarchists and nihilists committed innumerable acts of terrorism throughout the 1870s and 1880s, hitting a high watermark with the assassination of the Tsar in 1881.
ii) Alexander II’s assassination.
Assassination attempts were common throughout the 1860s and 1870s, but it was ultimately the revolutionary Narodnaya Volya that successfully assassinated the Tsar in 1881 (Evtuhov and Stites, 141).
The death of Alexander II greatly hindered government support for reform, resulting in renewed conservatism by Alexander III, anti-semitism, and more police attacks on suspected radical circles (not all of which had founding). The return to autocracy that marks Alexander III continues into Nicholas II’s reign.
A major backdrop throughout the 1870s on is increasing industrialization and, in the eyes of many reactionaries, Europeanization. The European/Russian debate is an incredibly persistent one in Russia, but the tenor of the debate for socialist groups had changed from a Slavonic ‘togetherness’ of the 1840s to a transnational revolution by the 1870s.
iii) The Russo-Japanese War and Revolution of 1905.
By the 1890s, there were several (largely underground) political parties, including the Social Democrats, which Lenin was a member under Georgy Plekhanov (who later rejected the soviets of 1905 under Trotsky; his role is rather contentious, see Baron). These movements crystallized in 1902-1903 with the First and Second Congress, leading to the separation of the Bolsheviks and the Mensheviks. Lenin, in 1902, invokes Chernyshevsky with a pamphlet entitled What is to be done? In 1904, the government official Vyacheslav Plehve was assassinated in Saint Petersburg (Evtuhov and Stites).The Russo-Japanese War does not originate these movements, but sets them off.
The Revolution of 1905 was precipitated by general strikes in Finland, and on January 9, a mass protest ended with hundreds of Russian citizens killed by police outside the Winter Palace. Dozens of strikes follow throughout the Empire, culminating in a general strike in Poland and the October Manifesto. All throughout 1905 terrorism, riots, and strikes are common throughout Russia, even on the battefield; Battleship Potemkin takes place in 1905.
Sergei Witte, who oversaw the industrialization of the state following the Russo-Turkish War, is a central figure in the 1905 revolution, the October Manifesto, and the 1906 constitution. As Prime Minister he was briefly succeeded by the conservative Ivan Goremykin, in turn usurped by Pyotr Stolypin, who had served as Minister of the Interior following the failures of the conservative Alexander Bulygin and Pyotr Durnovo (Durnovo, notably, anticipated the result of WWI and the dissolution of the Empire). Stolypin sought to preserve the monarchy by modernizing the peasantry. Stolypin was assassinated in 1911, marking the end of the fantasy to preserve the tsardom.
Nicholas II took an extremely active role throughout his leadership, for better or worse, in trying to curb and respond to radical movements.
Recommended Reading:
These are accessible introductions to Russian imperial history.
Evtuhov, Catherine, and Richard Stites. A history of Russia: peoples, legends, events, forces since 1800. Houghton Mifflin, 2004.
Seton-Watson, Hugh. Russian Empire 1801-1917. Oxford: Clarendon Press, 1967.
More specifically looking at the build-up to revolution, I recommend:
Fitzpatrick, Sheila. The Russian Revolution. Oxford University Press, 2017.
References:
Ascher, Abraham. P. A. Stolypin: The Search for Stability in Late Imperial Russia. Stanford University Press, 2001.
Baron, Samuel H. Plekhanov in Russian history and Soviet historiography. University of Pittsburgh, 1995.
Esthus, Raymond A. "Nicholas II and the Russo-Japanese War." The Russian Review 40, no. 4 (1981): 396-411.
Evtuhov, Catherine, and Richard Stites. A history of Russia: peoples, legends, events, forces since 1800. Houghton Mifflin, 2004.
Figes, Orlando. A people's tragedy: The Russian revolution 1891-1924. Random House, 2017.
Rabinowitch, Alexander. Prelude to revolution: The Petrograd Bolsheviks and the July 1917 uprising. Vol. 661. Indiana University Press, 1991.
N.B. There is a lot, lot more to cover on radicalism in Russia, and this is only a brief sketch of all the figures mentioned. I am more familiar with the 1840s, but if you have any followup questions I can try to point you in the right direction.