No, a proxy is not required to be inclined with the notice of annual meeting unless otherwise specified in your by-laws or house rules.

Keep in mind a proxy is not used to vote. It allows a shareholder to appoint someone else to vote on their behalf.

After signing in at the meeting, a ballot ( for voting) is given to shareholders. One ballot per unit and if another shareholder(s) gave you their proxy, you will receive one additional ballot for each proxy. I think you will find the below link helpful.

https://law.justia.com/codes/new-york/2016/bsc/article-6/

Our board has not sent out notices in regards to our annual meeting which usually is in May/June. Last year they cancelled it from June until October due to a problem in accounting. Our financials aren't ready yet and I feel they are pushing the annual until October again. It appears our board is running our cooperative in the ground due to lack of knowledge.What can we do in regards to putting us back on track? Doesn't the board have to have a vote from the shareholders about changing the month?

If a proxy is not included with your annual meeting notice and a shareholder wants to appoint someone to vote on their behalf, they can make up their own proxy by merely writing following on a piece of paper:

The name of the person who you are giving authority to to vote on their behalf IE: John Doe
The unit number/Apt Number
Print name of person giving their proxy: IE: Mary Jones
Signature of person giving their proxy IE” Mary Jones
Very important the DATE

the management company would mail out the proxies and include a memo that informed the shareholders that lived in the building that board member "x" would pick them. After board member moved, the managing company would mail the proxies out and told the shareholders that lived in the building to give them to the super to either mail them back in or give them to the super.
The week before the meeting they would post the same memo in the elevator and common areas the week before the meeting.

I had a problem with this since i knew that i as a shareholder could knock on doors or ask shareholders to give me their proxies. i notified the board members that lived in the building that this memo was incorrect , that the proxies could be given to any shareholder , and this was skewing the voting.
The managing company refused to give me contact info on the board members that didn't reside in the building.
The first 15 years the memo went out it was correct, it stated that if you were unable to attend you could give it to another shareholder who was attending the meeting or mail it back to the managing company.
The people who were running for election/reelection were also listed with boxes for the number of shares you wanted to vote.However the board member picking them up would tell the people to leave it all blank and just sign over the proxy to them.

By not allowing a shareholder who will not be attending the meeting to appoint whoever they choose to be their proxy violates Section 609(a) of the Business Corporation Law of the State of N,Y, which permits a stockholder to authorize any person or persons to act for them as proxy.

Even if your house rules and by-laws say different, the BCL supersedes. You should read your by-laws to see what is required for shareholders to call a special meeting for the express purpose of proper proxy procedures as well the procedure for the removal of director(s) with/without cause.

This link Will address your rights to names of directors.

https://law.justia.com/codes/new-york/2017/bsc/article-7/718/

The problem i have run into is there is no enforcement of the BCL .
I contacted my attorney generals office concerning mortgage fraud and they replied back that they do not do that. Referred me to the NYS AG office who had already proved unwilling to get involved in enforcing BCL and other cooperative problems. The mortgage fraud involved the cooperative informing buyers that the building was 90% owner occupied , when in fact it was lower than 50%.