write in XML dynamically

But I do not know how to write from textbox in flash to the xml file, or dynamicly create a xml from as3.

Flash alone can`t write to a users (or your own) filesystem you will need to look into AIR (publish your flash to AIR for Desktop to have access to the Filesystem). If you want the user allow to write a xml file serverside you will want to make use of a technology like php or asp in combination with flash.

use something like:

var objs:XML = new XML( <objects /> );

function addNameF():void{

var objname:XML = new XML ( <objectname /> );

objs.appendChild( objname); // add the <name> node to <objects>

objname.nodeValue = yourtextfield.text;

}