To fix the issue with the topics being set as unlisted, disable your Discourse embed unlisted site setting.
The issue with the topics not being published to the category that you have set is probably happening because the feed’s posts are not being served from the feed’s domain. You will need to look at the raw feed, by loading the feed directly in your browser. Once you have loaded the feed, look for the value of the feed’s link attributes. The domain that is used in this attribute needs is what needs to be added to the Allowed Hosts record that you create. Have a look at RSS Polling for details.
You can ignore that section of the Embedding page. That code is used for displaying Discourse comments on an external site.