The responses you suggest are likely too late. Jurisdiction challenges are waived if not raised in the proper time. Discovery disputes have to be raised at the time discovery options are pending. Now that the matter is in summary judgment stage, you must respond with evidence to create a "genuine issue of material fact" as that term is defined by New York statutes and case decisions.
If the plaintiff moved for summary judgment before you submitted your answer, you can still assert a defense of bad service. Similarly, if the plaintiff moved for summary judgment as soon as you submitted your answer, you can oppose the motion (in addition to stating all the facts to show that you don't owe the money) by telling the court that you haven't had a chance for discovery to develop facts that will aid you in your defense, and that the motion should be denied on that basis.
DISCLAIMER - THIS IS NOT LEGAL ADVICE, AND NO ATTORNEY-CLIENT RELATIONSHIP IS CREATED. THIS IS FOR GENERAL INFORMATION PURPOSES ONLY.