Hi Hartmut,
The WebView component of PixInsight is an excellent HTML5 renderer, as you have seen, but it is currently far from being a reasonably complete web browser. For example, the integrated browser in Process Explorer cannot download files or perform user authentication operations, or open multiple documents, which limits its usability as an actual browser considerably. It cannot represent or open PDF documents either.
WebView can render HTML5 multimedia objects (such as YouTube videos, for example) without problems, and can handle HTML5/JavaScript interactive content remarkably well, as the SubframeSelector tool demonstrates. But I still have to invest a lot of time and work to make it a real browser. This is in the to-do list, and you can expect more functionality added to WebView in successive versions of PixInsight.