Are all CE marked products tested and approved by European authorities?

No. In fact, it is the responsibility of the manufacturer to the assessment of the conformity of the products with the legislative requirements applying. The manufacturer affixes the CE marking and drafts the EU Declaration of Conformity. Typically, only products which are regarded as presenting a high risk to the public interest, e.g. pressure vessels, lifts and certain machine tools, require conformity assessment by a third party, i.e. a notified body.