May an attorney represent a client in Small Claims Court in New York State?

They sure can and do, I've done it myself! Many times. Usually I settle the case in the discussion rooms provided for preparing witnesses, etc., and when the case gets called, I just inform the court that the case has been settled. Note that if the other party fails to appear, you'll get a default judgment in your favor...whether you have an attorney or not.

In California, you are allowed to hire an attorney to guide you and answer your questions, but not to actually represent you before the judge, because this would defeat the whole purpose of small claims court. I would imagine it should be the same in NY. btw, you don't need an attorney, because small claims court is very informal and the judges are very understanding, even to those that don't speak English too well.

Yes.

"The Small Claims Part is a simple, inexpensive and informal court where people can sue for money without a lawyer. A claimant or defendant may hire an attorney if they choose to do so, but it is not necessary."

He/She can, but it is not needed. You can defend yourself and that is why it is called Small Claims Court. You might have a better chance of winning with the help of a Lawyer. I would get one.. Could be the party your suing, will have an Attorney.