>>We are trying to detect when the user clicks on, or moves the cursor using the arrow keys over two or more underline characters.
Please check the following article and write your own code.
In this article, it shows you how to get the window object and document object from editor.
Extending CuteEditor with its JavaScript API
>>We would like to raise an event, which will display additional input fields for the user to fill in outside of the editor
Please check this example:
asp.net Chat http://cutesoft.net/ASP.NET+Chat/default.aspx
Web Messenger: http://cutesoft.net/Web-Messenger/default.aspx
asp.net wysiwyg editor: http://cutesoft.net/ASP.NET+WYSIWYG+Editor/default.aspx
asp wysiwyg html editor: http://cutesoft.net/ASP
asp.net Image Gallery: http://cutesoft.net/ASP.NET+Image+Gallery/default.aspx
Live Support: http://cutesoft.net/live-support/default.aspx