Without a proper speed reference sensor signal, the DME relay keeps dropping out. Without fuel and ignition yes, the car does not run very well.
Why is there air in the system? I will guess because they removed the upper coolant hose from the rear of the cylinder head to the heater core in order to access the upper bell housing bolt easier. Doing this causes you to lose coolant and the resultant air in the system.
Also, when the ground for the sensors at the back of the engine block is loose, you get poor running as well as erratic gauges.
If your Porsche shop is unaware of these items, then perhaps they are not familiar with the 4 cylinder water cooled cars and you may wish to get your vehicle serviced else where.