On ifixit, all I found or on the net in gereral, al I found is how to fix the adaptoer itself. But what about the plug? It is my second time, the wiring inside of the plug itself came lose. But I don't seem to be able to open the plug to fix the wire, any idea how to fix it? By plug I mean the small end of the adaptor where the orange or green led lites up on the Macbook Air

Step 9-12 are totally unnecessary unless you need to replace a broken screen. All you need is to keep the front panel in a vertical position once the front is open. The battery can be removed without taken out the 3 connectors which by the way the screws are very very tiny and difficult to put back.