Can the police impound my car to administer a BAC test?

Yes.

Yes.

Yes.

In a DUI stop, yes, the officer has the option of impounding the vehicle and having it towed.

I would need more facts in order to answer this but porbably not.

They can impound it upon your arrest for DUI related to that vehicle. That is one of the normal consequences of DUI. A little free advice: When arrested for DUI, whether alcohol or drugs, then upon release from jail or booking the defendant is given documents that include a notice that you have only ten days to file a request with DMV for a hearing on an appeal of the automatic suspension of your license imposed by DMV upon your arrest. That is separate and runs consecutively with any suspension that may be imposed by the DMV, or the court upon conviction. Contact DMV and do so, timely if you think you have grounds for appeal, then appear at tne scheduled DMV appeal hearing and present any supporting evidence and testimony. If you don't know how to do these things effectively, then hire an attorney that does. When questioned, threatened, arrested or charged with any crime, the proper questions are, can any evidence obtained in a test, search or confession be used against you, can you be convicted, and what can you do? Raise all appropriate defenses with whatever witnesses, evidence and sympathies are available for legal arguments, for evidence suppression or other motions, or for trial. Low BA level is an arguable defense or grounds for motion. If you don't know how to represent yourself effectively against an experienced prosecutor intending to convict, then hire an attorney who does, who will try to get a dismissal, charge reduction, diversion, program, or other decent outcome through plea bargain, or take it to trial if appropriate.

I don't know on what authority they impounded the car. So I cannot say yes or no. There would have to be some justification of their actions to make them legal.

Most probably on the basis of the preliminary. Call with details and for an appointment.

Administering BAC has nothing to do with impounding your car. It was the arrest for DUI that gave rise to the impound action. If they had probable cause to believe you were DUI, they can legally impound your car even if your BAC later comes back under.