I agree with my colleagues. The death of the shareholder should not have a bearing on the existence of the corporation. the question now becomes who owns the shares and whether the pass under statutory rights of inheritance or if they are governed by a preexisting will.
If this is a case where the attorney was first counsel for the company then advised one of the shareholders(at the detriment of the company) there may be some ethical issues implicated here. As a general rule, an attorney must receive a waiver when representing two clients who may have adverse interests. If the clients consent to any necessary limitation on the scope of the representation and the potential future need for separate representation, and that the lawyer will be able to zealously...
Not enough here to really give an intelligent answer. Would need more facts but generally speaking this is an issue you should discuss with company counsel to see the best routes for raising funds whether it's through debt or equity.
The short answer is yes. In addition, you will need to have a NY franchise tax exemption as well and a NY sales tax exemption. There is a good bit of tax exempt documentation required for the 501(c)(3) application and you should have an attorney review your files before submission. This can save you plenty of time in the process and answer most of the questions you have in connection with establishing your 501(c)(3).