Question 1: Is it a plugin or hack that can allow one to parse html inside the visual view
Neither of both. The visual view is the visual view and not the HTML view. If you want to paste HTML, use the HTML view.
Question 2: Is it possible to insert html code to the html view from a popup initiated from the visual view
Technically this should be possible, but it would mean that you need to create a plugin with javascript for that first. In case “hack” from your first question is about writing a plugin, then well, this could be done for visual view as well.
The TinyMCE API is a good start for doing that stuff.
This answer to the “Want to have the Post editor remembering the last editing position” question might be helpful as well.