When looking at a specific level 2, other level 2 sites are showing up in the Referrer sites, won't they be counted twice?

Traffic sources cannot be counted twice. A visit can only have one source, and as such the visits with an "Other level 2" source and a "Referrer sites" source are independent from one another.

That said, we would like to explain why you may be seeing your own site's domains and URLs in your Referrer sites.
When visiting a site, the URL of the previous page is kept by the browser, and that value is what we use to automatically populate our tag. When the previous page sent a hit that is part of the visit, that value is discounted in favour of the visit's source. When you're looking at a specific level 2, a visit is given an "Other level 2" source if the user started on a different level 2 site and came to the current level 2 within the same visit.
However, if a page is reloaded after the visit max duration has been exceeded, a page hit can be sent with the URL of a page from your site as the referrer (as populated by the browser) which we will not be able to match to a page hit and will classify as a Referrer site source.
This can be verified by looking in-depth at the behaviour of one of the visitors whose visit's source was classified as "Referrer sites" despite the referrer URL being from another level 2:

As you can see from the above screenshot, the visit max duration of 30 minutes was exceeded between 08:47 and 09:24, thus a new visit started upon the user reloading the page (denoted by a new visit ID). The referrer for visit ID 201 is the URL of the page viewed first in the user's journey, as the value was kept by the browser.

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