Discourse comments can be embedded on other sites, for example:
A WordPress plugin exists to make the process very straightforward, other CMS require slightly more hands-on implementations.
In each case when users wish to comment on a post they are directed to the Discourse site to make their contribution.
In terms of controlling who has access to the comments, that’s really down to how you secure your sites. As for ownership, users own the content they create, that’s the law. They assume the copyright on their works at the point of publishing/creation. The terms of your sites will determine whether you have a license to re-use the things they post.