You can serve a discovery demand requiring that plaintiff provide you with all relevant contracts, emails, documents, etc. dealing with the subject...

It should be labeled an Affidavit in Opposition to Cross-Motion and In Further Support of Motion. You are entitled to submit papers in Opposition...

Summoned to serve a notice of appearance on the plaintiff's attorney?

No. You may serve the Notice of Appearance, or your Answer or Motion to Dismiss, by mail to the plaintiff attorney's office, and then file same...

Not necessarily. It depends on the nature of the claims asserted.

Do both parties need to file a Note of Issue? In this case the Plaintiff already filed one. I am the Defendant.

No. Only one party files the Note of Issue although you can promptly move to strike it if discovery is incomplete.

If im the plantiff in a civil case, And i have to attend a Depositon do i have to answer every question im being asked?

You can answer that you do not remember, or that you have no present recollection, so long as you are being truthful. Generally speaking, you do...

Do I have you to show up in court

Yes, but touch base with attorney who issued the subpeona to coordinate timing.

When we submit motion or cross motion, do the Judge really read them all? Or do they usually just take a look few mins before

Generally speaking, either the Judge or the Law Clerk will, in fact, read the papers before rendering a decision. However, depending on the Court...