Er, I'm pretty sure that’s not what “canonical” means . . . (Yes, Google does recognize cross-domain canonicals, but the assumption is that both domains belong to you.)

A Canonical link signals to search engines, that the two pages may not be exact copies, but are essentially the same, and thus when someone is looking for either of these pages please show the page in the link instead of the other one.

The good news is, Google often ignores these links if the content does not appear to be similar. Pointing a canonical to a different domain is most likely enough of a reason for Google to ignore the link. So the canonical links are most likely not doing anything for you. Removing the links will certainly no cause any harm.

Canonical links are typically used when content is customized based on some user input. The user may want to share a link or refer back to the page, so having a "page" for the content is required. But the content of the page is marginally different to a generic page but the difference does not provide sufficient value to other users, so one likely wouldn't want search engines sending new users to that page. Adding a canonical link from the customized page to the generic page solve the problem. The search engines then know that the preferred page is the generic page.

Well then I was mistaken.

I was under the impression that when I use an article from another website on my own website and rewrite it, I would still have to use canonical to let google know that their article is the original one...

A canonical URL is the URL of the page that Google thinks is most representative from a set of duplicate pages on your site. For example, if you have URLs for the same page (for example: example.com?dress=1234 and example.com/dresses/1234), Google chooses one as canonical. Note that the pages do not need to be absolutely identical; minor changes in sorting or filtering of list pages do not make the page unique (for example, sorting by price or filtering by item color).

The canonical can be in a different domain than a duplicate.

Consolidate duplicate URLs [developers.google.com]

Using the canonical tag, you can steer Google toward preferring one URL over others. Otherwise, Google will make that choice for you, so using the tag is not even strictly necessary; it's just a tool in the SEO toolbox.

A link to the source article should be sufficient in terms of attribution.