Pretty much everything you need to know about the ownership and licensing of your material on Medium is in the Medium TOS you contractually agreed to when you signed up with the service. Basically, you granted Medium a license to use the work, but you did not agree to an exclusive license nor turn over copyright to them.
Part of that Terms of Service – Medium Policy reads:
Content rights & responsibilities
You own the rights to the content you create and post on Medium.
By posting content to Medium, you give us a nonexclusive license to
publish it on Medium Services, including anything reasonably related
to publishing it (like storing, displaying, reformatting, and
distributing it). In consideration for Medium granting you access to
and use of the Services, you agree that Medium may enable advertising
on the Services, including in connection with the display of your
content or other information. We may also use your content to promote
Medium, including its products and content. We will never sell your
content to third parties without your explicit permission.
You’re responsible for the content you post. This means you assume all
risks related to it, including someone else’s reliance on its
accuracy, or claims relating to intellectual property or other legal
rights.
You’re welcome to post content on Medium that you’ve published
elsewhere, as long as you have the rights you need to do so. By
posting content to Medium, you represent that doing so doesn’t
conflict with any other agreement you’ve made.
By posting content you didn’t create to Medium, you are representing
that you have the right to do so. For example, you are posting a work
that’s in the public domain, used under license (including a free
license, such as Creative Commons), or a fair use.
We can remove any content you post for any reason.
You can delete any of your posts, or your account, anytime. Processing
the deletion may take a little time, but we’ll do it as quickly as
possible. We may keep backup copies of your deleted post or account on
our servers for up to 14 days after you delete it.
Pertaining to presenting Medium content in an iFrame on another site, this is reasonably close to not allowing that:
You may not do, or try to do, the following: ... (2) access or search
the Services by any means other than the currently available,
published interfaces (e.g., APIs) that we provide;...
You can use Embed Code Generator | Embedly to embed an iFrame of a Medium page on another site. But contacting Medium via the email at the bottom of the TOS would tell you for sure if it is OK.
Comments on your pieces on Medium do belong to the owner.
And
You own the rights to the content you create and post on Medium.
appears to cover the idea of copying your material from Medium to your own site. If in doubt, ask them.
