I used to host with godaddy, their control panel is a nightmare. It takes forever to get in there and get anything done. That was the main reason I left and moved to host gator.
Anyway, their text editor in the file manager is what is known as a WYSIWYG editor (What You See Is What You Get). Anytime you do a line break it inserts a <br> tag in the html among other things.
Yes, you should just go into the actual page yourself and make edits there. Once you track down the persons name in the code you should do just fine with the edits. As Stevie mentioned though, be sure not to tamper with any of the html elements shown in brackets.
Obviously you have your username and access to the file manager so you could actually set up a FTP client from your local machine and take care of everything from there. You may want to make other changes in the future so I think it would be worthwhile to set up an FTP.
I use Core FTP Lite, it's free.
If your on Windows you could use Notepad to edit the html but there is no syntax highlighting so it might be hard for you to navigate through the code.
I would suggest downloading a free text editor such as [Notepad++ or [URL="http://www.pspad.com/en/"]PSPad ](http://notepad-plus-plus.org/)since they will highlight the html elements for you. That way you can see them easily and stay away from them.
With an editor and an FTP client (and your account passwords) you can take care of everything yourself and keep a copy of all your files on your local machine.
Just make edits and upload them straight to your site without godaddy's control panel.