Generally speaking no, though they can usually get unemployment for days during the school year they don't get called in. In some cases, they may be able to collect unemployment during summer break...
YES, provided the unemployment benefits are properly yours.
In other words, that you worked and made the proper contributions from your income to the state fund. Having a state pension is no...
Please see the link for the NYS Dept. of Labor, Unemployment Insurance: How to file a claim and the Benefits Online Page. You can also call their toll free number at: 1-888-209-8124 for New York...