A: The fact you were unable to physically move your car will probably not be a defense to dismiss the ticket. However, sometimes, a parking ticket is written defectively (missing some info or containing inaccurate description, etc.), which can be a ground for dismissal. Also, you can dispute the ticket online (with certain conditions to be met), and that may eventually have the city to lower your fine. Retaining a lawyer may not be financially feasible for this case. Wish you the best.
A: No. Speeding violation is a speeding violation which is a traffic violation. Reckless driving in NY is a criminal offense (misdemeanor). If the officer had intended to issue a summons for Reckless driving, you would have got one independent of the speeding ticket.
A: If your son and his friend were charged with § 140.05., then it's a violation, not a criminal offense, but it has a potential jail time if convicted. You should know that the People (State) are obligated to prove every single element of the charge and your son has no duty to disprove anything.