Do i need a lawyer for small claims court?

You don't need an attorney (although it is usually a good idea to at least consult one when dealing with legal issues), unless the car was owned by...

Can a court put a case back on after it was dismissed for nobody showing up because the court calendared it wrong?

This is not a common situation, but the court does have the power to put the matter back on the calendar.

120 days is 4 months and I don't know if you count the day you buy the index number, etc

You would start counting on 4/17/14 (i.e., the day after you purchased the index number).

I am the petitioner in a proceeding -two of the three defendants didn't appear on the returnable date or oppose my petition.

It is not clear what type of proceeding it is, which may affect how you can or should proceed. However, if it is a lawsuit in which you are the...

NYS civil suit. At depositions, plaintiff's atty didn't depose me.

It's a risky strategy, regardless of the reasons. One of the main purposes of discovery is to find out what evidence (documents, testimony, etc.)...

An affidavit from new counsel in and of itself is not new evidence. An affidavit from new counsel actually citing new evidence would be necessary....