TextEdit app always opens with File Open dialog

You can open up a textedit instance as root by entering the full path to the actual executable :

sudo -b "/Applications/Textedit.app/Contents/MacOS/TextEdit"

Once your root instance is open you could browse to the file you need or do this from the command line :

sudo su - root -c "open -e /etc/apache2/httpd.conf"

The only way to do this with all file types is to create a service in automator, which actually should make things easier for you.

1. Open Automator and select "Service".
2. In the "Service receives selected..." dropdown, change it to read "receives selected files and folders in any application"
3. Select Utilities from the library menu in the left pane and double-click "Run Shell Script"
4. Change the "Pass Input" dropdown to "as arguments"

5. Delete the default script and replace with the following:

   if [ -f "$1" ] ; then
       open -a "TextEdit" "$1" ;
   fi
   

Save this file as whatever you want it to show up as in your contextual menu, something like "Open With TextEdit" and you're done, you'll now have the option to open any file with text edit.

It won't be in the open with menu, it will be a separate item in the contextual menu grouped with any other services you have running.

On a side note, if you're developing on a mac you should really think about using a better text editor like TextMate or TextWrangler or Sublime Text, some of these even add the service for you to save you doing all of the above.