If the keys were in the ignition, the engine was running, and the car was parked on a public street, that still is considered "operation" under the DWI statute. Sounds like you have some mitigating circumstances, however. Presumably, you have an attorney who has brought these factors to the attention of the prosecutor.
Yes, but this is a very tricky area of the law and can not be answered adequately without knowing more facts. It depends who has primary jurisdiction. For someone who has been in continuous custody from the time of arrest, it is the jurisdiction which arrested the defendant first. To ensure concurrent sentences, you want the state sentence to be imposed first.
I agree with the advice the police gave you: hire a lawyer. If this is your first offense, you are eligible to be treated as a youthful offender, which means the record of conviction will be sealed. For a first offense on a charge of this nature, a plea to a misdemeanor is the standard deal, unless there are aggravating factors you haven't disclosed. With some effort on the part of your lawyer, you may be able to get the charges reduced to a violation, but that is a stretch. I don't see how...
a) agree with counsel, you have to first ask your lawyer, b) you have to check the court file, c) what level offense is it (A, B misd, felony), d) depends what kind of a record was made concerning the nature of the officer's injuries - it may or may not be excludable depending on whether it was the kind of injury that would have prevented him from testifying. Your lawyer will have to make a motion, and then their will probably have to be a hearing regarding the nature of the officer's injuries.