My understanding is that it is not possible to fully embed Discourse in an iframe. That question has been asked and answered multiple times on this forum.
You can embed Discourse comments on your site. That can be done by following this guide: Embedding Discourse Comments via Javascript, When comments are embedded, users will still need to visit the Discourse site to create a new comment.
There is also a new feature that allows you to embed a Discourse comment list on your site. There are details about that here: Embedding a list of Discourse Topics in another site.
The other option for getting Discourse content onto an external site is to use the Discourse API to pull data from Discourse. That is the approach that our WordPress plugin uses.