The TextArea can be filled like many others component by adressing the .text property.
Then to open your xml file and read it, you must create an XML object and describe how to behave when the file will be loaded, that means what to do when the file has been read with the onLoad
myObjectXML = new XML() ;
myObjectXML.ignoreWhite = true ;
myObjectXML.onLoad = load_XML_function ; // what to do when the file has been load
myObjectXML.load ('news/current.xml) ; // that's tell where is your file and it's relative to you .swf
So it means that you have a load_XML_function
somewhere in your class in which you will extract the content to put it in your textArea.text. It's probably a loop whell you will from the top to the bot with some nextSibling
They are different scenarios depending on the structure of your file
I hope it's helpfull !