If you set EmEditor to run as Admin, and you are not logged in as admin, that will cause issues. You cannot drag a file from one non-Admin application (e.g. Explorer) to another Admin application.
Generally, Run as Admin should be used for applications (or utilities) that need special access and/or don’t require much user-interaction. EmEditor, on the other hand doesn’t need special access (AFAIK) and requires regular interaction.
The other issue, you didn’t mention whether you installed Win7 32bit or Win7 64bit. You will need a 64bit context-menu handler if it is Win7 64bit.