What about paid language lessons? Can I promote those in the Exchange?

As language lessons are included in the scope of the Exchange, and there is no dedicated area of the platform to offer paid language lessons, the Exchange is the most adequate place to do that.

Until there's a dedicated platform area for language training, you can feel free to promote your language lessons using the Exchange. If that were to change in the future, an announcement would be made in the Translator Coop forum.