As far as I know, there is no way currently to create arbitrary notifications via the API, so I don't think the dashboard will be able to create notifications unless / until that gets added to the MediaWiki notifications system.

Is there a way to send an e-mail? That would be practical in some cases.

The Wiki Ed dashboard sends emails, but the email features are not planned to be enabled for the P&E Dashboard at this point.

That is a pity. I wonder, is that because it would be very technically demanding or because it was decided so?

It's mainly to avoid asking users to go through the signup form where they put their names and emails, which we use on the Wiki Ed site.

And the Dashboard is not able to "see" the e-mails of the Wikipedia accounts or use the "special:e-mail" page...

Hmm this is one of the reasons an external tool will never be as good as our Wikipedia extension :-(. It cannot send notifications or e-mails.

I wish we talked about such caveats before and not now when the tool is going to be deployed and offered to affiliates.

It should be possible to use Special:Email, I think. It would just take some development work to hook that up.

Not actually Special:Email, but it is possible to send emails through Mediawiki via the API, I think.