Thank you for your question. Having only one piece of one half of the story, I can't responsibly estimate whether you will have your case dropped, so I should start by saying that because the nuances of every case are different, this information should not be relied upon as complete or advice without consulting in person with counsel. But that said, please allow me to discuss the law and perhaps that will shed some light on your situation.
1. A police officer only needs probable cause
to believe that someone has committed a crime in his/her presence to effectuate an arrest, so an arrest with probable cause might be an abuse of discretion, but it wouldn't be illegal as long as there was probable cause. Allow me to emphatically state that you made the right decision to not answer his question. But yes, this officer is a jerk. Personally, I would complain to his supervising Lieutenant.
2. There is some overlap between MIP and MIC charges. I can't say whether an officer's oral misstatement would affect the outcome of any given case, but it normally would have no impact whatsoever. It would be similar to calling it "drunk driving" instead of "driving under the influence"--what ultimately matters is what goes on paper.
3. Miranda rights do not have to be administered in most arrests. The function of Miranda is to protect individuals from having their statements used against them while in police custody and while being interrogated. Miranda is only relevant if a suspect makes a statement while in police custody, while being interrogated, and the prosecution wants to use that statement against the suspect in court
. If all of those elements are not met, the failure to administer a Miranda warning would have no legal consequence.
All of that said, there can be no conviction without proof of guilt beyond a reasonable doubt, and the failure to answer a police officer's questions generally cannot be admitted into evidence in court. So you're walking down the street and you are charged with MIP because your friend has beer in his backpack. Possession generally means that the defendant can exercise dominion over the paraphernalia and knowledge that it is there. What evidence is there that you consumed, acquired, or possessed liquor? May I safely assume that the backpack was closed? How do you prove beyond a reasonable doubt that you knew your friend even had beer in his backpack?
I don't know the strength of the prosecution's case in your specific matter for reasons previously discussed, but it's certainly possible that the case will be dropped when you appear in court, if not dismissed thereafter.