How do you open up two instances of HTML editor at one time? I often want to copy something from one page to another and when I try to start another session, nothing happens until I close my first session.

Why would you need that? There are tabs at the top of the program that will allow you to open the page you want to paste too..

Using Visual Studio, I have CoffeeCup as my default HTML editor, so when I open up two projects i need to edit the HTML templates within each project.

So just open the pages that are needed to be edited an leave them on the tab.