Yes, please.
In this phase, the New York State DMV sended CLP holders a notification if their medical certification status appeared as "Not Certified", after which the CLP was canceled if the CLP holder didn't re-certify within 55 days.
Can the NY State reject my application if I have an open suspension in another state?
Yes. With the CDL Permit Rule the NY State can check for open suspensions and revocations in other states and reject any application if it finds open suspensions.