You need to speak to a NY attorney. If you plead in NY you are very likely to be suspended in NJ.

Yes, driving without a license can affect or delay you getting a license. You should retain or consult an experienced attorney.

An experienced attorney could help you reduce your careless to zero points since this is your first moving violation.

It depends on your Lease. More information is need. You should retain an attorney or at least consult with one.

You may want to think about retaining an attorney who may professionally handle this matter on your behalf. From your description, it might be...