Tolstoy seems to be thinking of something like this statue of an Egyptian family, where the hands are resting in the laps of the three figures.
The particular roi de Prusse (king of Prussia) in question is Frederick the Great (1712-1786). Although as a child he showed little interest in warfare, after Frederick II ascended the throne Prussia won a string of military victories over its neighbours, Austria and Poland.
Like Catherine the Great in Russia, Frederick was interested in the Enlightenment philosophies of France, especially that of Voltaire, with whom he corresponded for many years. Like Catherine, this did not prevent him from ruling as an absolute monarch over his subjects. However, during his reign he modernised Prussia, improving the economy and pushing it to the forefront of European politics.
Frederick was a talented musician who composed four symphonies, and a hundred sonatas for the flute. He had a reputation as a micromanager, who would oversee every aspect his household's daily life; Prince Bolkonsky shares this obsessive trait. Tolstoy's grandfather Prince Volkonsky, upon whom the character of Prince Bolkonsky is based, served as an ambassador to Frederick II from the court of Catherine the Great.