First, you can not have missing or loose bolts from the exhaust manifold because it will have an adverse effect on your air fuel ratio causing incorrect fuel delivery. It must be repaired no exceptions or you can risk burning a valve among other things and that's likely why you are seeing the irregularity that you described.
One reason you have significant power loss is because all cylinders are not firing. I can hear a skip clearly in the video with the motor running. Fix the exhaust leak and check that you haven't crossed wires and for a bad ignition part, etc.
Just finished watching the whole video, that piece of pipe in your exhaust will kill any hopes you have of performance if you drove it that way.
[This message has been edited by Joseph Upson (edited 09-02-2013).]