Can a police officer administer a breathalyzer on a 17 y/o?

The short answer is yes.  The longer answer requires much more context.  If they had reason to believe your child is under the influence they can do a beathalyzer, which is inadmissible for anything but the presence of alcohol.  There is no statutory requirement that they inform you that the test was done.  If your child has been charged with underage drinking or DUI there are a lot of facts and circumstances that could make the case triable.  If your child has been charged consult with a local attorney who can help you minimize the amount of damage such a case can do to someone's record.