How can I set the properties for the text outline / border for each character in a line of text in AS3 ?
I don't think you can. What you can do is use a blur filter to mimic the appearance of an outline. Just paste this into an empty AS3 movie:
var txt:TextField = new TextField();
this.addChild(txt);
txt.appendText('Lorem ipsum');
txt.autoSize = TextFieldAutoSize.LEFT;
txt.antiAliasType = flash.text.AntiAliasType.NORMAL;
txt.selectable = false;
var txtFormat:TextFormat = new TextFormat();
txtFormat.size = 40;
txtFormat.font = 'Helvetica';
txt.setTextFormat(txtFormat);
txt.defaultTextFormat = txtFormat;
var outline:GlowFilter = new GlowFilter();
outline.blurX = outline.blurY = 1;
outline.color = 0xFF0000;
outline.quality = BitmapFilterQuality.HIGH;
outline.strength = 100;
var filterArray:Array = new Array();
filterArray.push(outline);
txt.filters = filterArray;
Try playing with the strength, blurX, blurY and quality properties, in order to obtain different appearances. I think that's about the closest you can get to a text outline.
PS: font embedding would greatly improve the quality of the effect, as well as making the antialias work properly.