In a few words. The engine is fitted to the aircraft by us engineers and once all connected to the aircraft itself, we ground run the engine. This involves starting the engine and ensuring it meets all the correct figures. If it meets the correct figures, we sign up and let the drivers take it away somewhere far away!! If by chance it fails to meet these figures, then its back to the hangar for adjustments. This job is usually a hangar job but us lineys sometimes have to chip in. I recently changed a UPS B767 engine. Good fun.
When running high power checks, yes, you do run the other engine but usually at idle. But please someone correct me if diff for some a/c. And we have to sit on the brakes to stop her rolling forward.
Cessna24