Your rights are to be found in two places: your bylaws and NY state law.
Shareholders cannot "manage" a corporation, for various legal reasons, but elect directors to manage, and the Directors appoint the officers who do the day-to-day.
You almost certainly have a right to the names and addresses of all 22 shareholders. You may or may not have a right to a copy of the financial statement. You don't really say what the arrearages are related to so there are numerous possibilities.
If it's really important to you to correlate the uncollected arrearages, you may ulitmately have to join with others and hire a business litigator.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
You should find the enclosed piece very helpful to you as it gives statutory citations to those areas of the law that you can use to assert your rights with the Board (including access to books and records). A phone call to the AG's office once you get up to speed form the enclosed will get you a better game plan on how best to proceed, especially if you can get 5-10% of the other homeowners to join you in a specific course of action.
My answer is not intended to be giving legal advice and this topic can be a complex area where the advice of a licensed attorney in your State should be obtained.