Is it possible to create a WiKi on an organization level in GitHub? That is, I don't want a wiki in a single repository and I want to avoid creating a new empty repository only Wiki. Instead I want to create a Wiki for a whole organization. Possible?
One option could be to create a GitHub pages repository and then create the Wiki there.
This article suggests to create a dedicated repository for the Wiki: https://labs.inn.org/2014/05/19/applying-git-to-github-wikis/
Github is a repository management system, not an all purpose hoster. You'll have to host your Wiki either on your own servers or on a hosting account you purchase.