In Dostoevsky's Idiot, it seemed that it was perfectly legal to publish articles of slanderous nature.
Was there any legal protection of a Russian's rights in publicity in the 1800's?
Russian law in the 19th century was probably derivative of Roman law which is explained at page 594 of this 1903 law review article, because almost all countries in continental Europe at the time ultimately derived their substantive law from Roman law.
There was a minor crime at Roman law for offensive statements, without regarding to the truth, and a tort at Roman law for false private statements, to which truth was a defense. Many countries at that time, probably Russia among them, also had special criminal offenses for insults to royalty and aristocrats.
The right of publicity is a much later American invention than defamation law and developed in connection with the modern advertising agencies at common law in response to commercial ventures that sought to exploit professional models. It is unlikely that this tort would have existed in 19th century Russia.