Does the motor need to be running to be charged drunk driving?

No. But the prosecution will have to prove that you were operating the motor vehicle. They will have a harder time proving their case.

If the car is stopped and not running, most courts say that the car was not being operated.

In California, the answer to both your questions is no.

The question gives an inference of a possible defense.

Depends. If it can be proven when driving happened, through witnesses or other information, no. Huey's don't have to be in ignition to be charged with DUI.

Yes, you can be charged with DUI even if the motor is not running.

Not only does the motor need to be running, but the car needs to actually be moving. Some states have operating under the influence statutes which allow prosecution for being in or around the car while drunk. California requires what's called volitional movement of the vehicle to obtain a conviction. I like to remind cops, prosecutors and people that the "D" in DUI stands for driving and they must prove that the person charged was driving to obtain a conviction. There are a couple of exceptions to the driving requirement and those are covered under Vehicle Code Section 40300.5. For instance, if you've been in an accident or if the car is blocking the roadway, then the cops don't need to see the car move. Without a witness to driving, the prosecutor can't establish time of driving. Without time of driving, the defendant's blood alcohol content at the time of driving, necessary for a conviction, cannot be proven. In addition to the requirement to prove Driving at trial, the common law and Penal Code Section 836 require that a misdemeanor offense occur in the presence of the cop who makes an arrest for the arrest to be lawful. A DUI cannot occur in the officer's presence, if he doesn't see (sense) driving.

No to both questions. Generally there is observed driving which attracted the officers attention or is perhaps reported by a witness third party.

Yes, and it also has to move. But remember they can use circumstantial evidence to show you must have been driving just a moment prior. You need to hire a DUI specialist, and do it soon because you have only 10 days to save your license.

Generally speaking, no, the motor does not need to be running when a person is arrested in order to be charged with an OUI. However, it may be harder for the prosecutor to prove the charges beyond a reasonable doubt when there is less circumstantial evidence supporting the elements of an offense; and notably, whether the accused was operating a motor-vehicle is a key element in some cases. These are very complicated factual questions and they depend on the alleged circumstances. Ultimately, these are factual questions and possible issues for a motion, so you would need to privately consult with a lawyer who has full access to your file.