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This could be anything from an electrical fault to a fuel pump issue or a major air leak/loose hose clamp problem. If the check engine light is not on and there are no fault codes stored , a good start would be to confirm fuel pressure at the time the failure occurs. Fuel pressure is one of the few parameters not directly monitored by the on board diagnostics. If I understand your comment "All lights come on but none stay on" correctly , the electrical portion of the ignition switch ( a common trouble spot) could be failing. Short of replacement a simple , but not absolute , test can be wiggling the key with the engine running to duplicate the malfunction. Remember , you need air , fuel and ignition for the engine to run....
As an aside the turbochargers can only be replaced in pairs since they are computer matched. In addition there are several critical components such as oil lines that must be replaced concurrently.
If the misfire is ignition related you may have a crack or electrical fault in the ignition coil. With the engine running spray the ignition coil and cables with a mist of salty water. This will "stress" these areas of the ignition system. Any electrical leakage will become evident as an immediate misfire or visible electrical arcing. If you have access to an appropriate scan tool you can confirm fuel mixture , if it is random multiple misfire fault or a specific cylinder misfiring. The direction you take in repair starts with that information.
Replacing both horns should take about 1.2 hours. The part price varies depending on your source. Genuine Audi horns are about $100 each , aftermarket probably less .
Since your check engine light is not on and everything else that uses the speed sensor signal is ok you may well have a problem in the instrument cluster itself. A good place to start would be to remove the instrument cluster and confirm all the connections at the cluster itself. Inspect the wiring and connectors as well as the physical attachments at the cluster. If you have a wiring diagram and digital multimeter or scope you can confirm a steady signal at the cluster. You may have a failure at the instrument (speedometer) , or simply a poor connection. The speedo signal can be monitored with a scan tool as well. Often the act of disconnecting and reconnecting the instrument cluster will restore operation.....
Look under the left fender , under the fender liner (black plastic) near/behind the spring. Their is a metal cable with a loop in it. Use a hook type tool to grab it and pull. Hood should release. The cable is tucked away , but it's there. You will need to remove the wheel and maybe pull back the liner to accomplish this. Not something done on the side of the road.....
If the immobilizer logo , it looks like a VW beetle , in the instrument cluster is flashing when the engine starts it is indeed an "alarm" issue.....
If you're confident the oil pressure at 2200 rpm is above 22 psi , at operating temperature , you either have a failing high pressure switch , the one located on the head , or a failing control unit in the instrument cluster. Remove the electrical connector from the oil pressure switch and place a 12 volt test light between the switch and the battery positive post. The test light should be on. Start the engine , increase engine speed. The test light should go out at around 2200 rpm. If not , the SWITCH is bad. If it does go out you may well have a problem in the cluster. As a footnote when the test light is on or off , it should not flicker. If it does The SWITCH is bad.
this can occur if there is water in the brake booster. drainage issues in the plenum area , usually caused by leaves blocking the drains , allows water to accumulate and enter the vacuum booster. freezing conditions obviously turn the water into ice , which will jam the booster/brakes internally. warmer temperatures thaw the ice relieving the blockage. you need to replace the brake booster after confirming this diagnosis and repairing the root cause of the problem , water in the plenum.
audi brake pads should be replaced when their is <4mm pad material remaining. there is a tool to measure the wear without pulling the wheels. incidentally 4mm is the maximum thickness at which audi warranty will cover brake pad replacement