I've read about sending a page to a mediawiki using libre writer.
But is it possible to call up an existing wiki page, edit it and send it back to the wiki?
If so, how is this done?
As far as I know there is no such option, the connection is one-way only. In some cases you could be able to convert WikiText e.g. with
pandoc. For a local wiki it is a possible workflow to keep the Writer documents, and only use them for export.
Another workaround is using the new visual editor of MediaWiki, which I find quite user friendly in comparison with WikiText.