Everything you are looking for more or less exists now, except for your fourth requirement. Replies to the post can only be generated on Discourse, not on WordPress. This is by design, but I’ve been wondering if it’s time to change that.
It would be technically possible to allow users to create comments on either WordPress or Discourse if WordPress was configured to be the DiscourseConnect provider for the Discourse site. It would take a fair amount of work to get this right, but I can see how it could be useful for the case where Discourse is functioning as the comment system for a Discourse site.
I’m not sure if this distinction makes sense to others, but the way I’ve been thinking about this is to make a distinction between comments and discussions. Replies to a WordPress post (or any embedded post) are probably better thought of as comments than as being part of a discussion. The advantage that Discourse offers over traditional comment systems is that comments could become the starting point of new topics that actually are discussions. (I’ll post about this in more detail in a separate topic soon.)