Correct me if I'm wrong, but as I understand it an Emperor was considered to be somewhat of a higher title than a King. So, was there an outcry when suddenly the Russian Tsar autoproclamed himself Emperor? And by the way, was tsar a title equal of that of a king?
Peter the Great was proclaimed 'Emperor of all Russia' and the position lasted from 1721 - 1917, the position wasn't really self proclaimed, but instead it was decided by the Russian senate and synod (governing body of the Russian Orthodox Church). All the title really meant was that the Russian citizens had to accept the Tsar's autocracy.
Peter and all of the following Tsar's were seen as the ruler's of the Russian Empire. Emperor and Tsar mean the same thing, the literal definition of Tsar is 'Emperor of Russia before 1917'. I'm not too sure on the reaction of other European monarchs on the actions of the Synod and Russian senate, but if the land was owned by Russia, what difference does a title make? Source: I am a college student studying Tsarist Russia. Ifs my first time posting here so my information may be fairly skewed, please feel free to correct me.
Seems like there's no one to answer, at least, I might help you with your second question about a tsar title.
Due to different naming of titles in Rus and the rest of Europe, the same title was viewed differently. In Rus and, later, Russia the grand prince title was viewed as the king title. Thus, the tsar title supposed to be the same as the emperor, as before that only the ruler of the Golden Horde was named tsar in Russian chronicles. After the conquest of Kazan and Astrakhan khanates under Ivan IV the imperial ideology was fully formed. On one side, in the "Moscow is the Third Rome" concept it tapped into the Byzantium heritage, as Ivan III married Sophia Palaiologina, whose uncle was the last Emperor of Byzantium, and Russia being the strongest Orthodox(i.e. "the true faith") country became the defender of faith. On the other side, by taking Kazan and Astrakhan, it tapped into the Golden Horde heritage, claiming it "by the right of conquest"(similar to how the Ottomans called themselves the Emperors of Rum after taking Byzantium).
But from catholic Europe's perspective, prince and grand prince titles corresponded with duke and grand duke ones, thus the tsar title was viewed as the next step from the grand duke which is the king title. Also, latter failures in the Livonian war, Moscow being burned by Crimean khanate in 1571,and the time of troubles of the early XVIIth century didn't help Russia in being perceived abroad as the strong empire.
So, from the perspective of Peter I, calling himself an Emperor was a form of reinstating the position claimed 2 centuries ago.