Short answers, pulled from the story.
Peter the Great opened his personal collection to the public in 1714. This event marked Russia's first public museum and established a new tradition for imperial courts across Europe.
The present Kunstkamera building is a turreted structure designed by Prussian architect Georg Johann Mattarnovy. Its foundation stone was laid in 1719 and it was fully completed in 1727.
Albertus Seba sold his collection to the Russian court in 1716 while Frederik Ruysch did so in 1717. These transactions significantly expanded the original holdings beyond what Peter had gathered personally.
Peter encouraged research into deformities specifically to debunk superstitious fears about monsters. He issued an official ukase ordering malformed stillborn infants to be sent from anywhere in Russia to the imperial collection.
The Kunstkamera collections were dispersed to newly established imperial museums during the 1830s. The most important new entity was the Peter the Great Museum of Anthropology and Ethnography established in 1879.