Can a cop write tickets for parking in a fire lane in new york state?

yes....

Traffic violations

Hard to get a workable answer for a case like yours on this forum. This is something that requires for a traffic ticket attorney to review in...

?

You can't sue them. You can have an attorney go to court instead of you and get them reduced to perhaps dismissed.

I was stopped for not stopping at a stop sign that I thought was a yield intersection.

Plead not guilty and then perhaps you can a plea offer to no points. You can also retain an attorney to go court instead of you.

What might happ?

Driving without insurance is very serious violation. Do not trust cops who say it "would probably be thrown out."

Eventually you will get a notice that your license is getting suspended for failing to appear. Further down the line you you be convicted by...

How can I fight this?

Where there's an insurance lapse it triggers an automatic registration suspension. However it sounds like he just gave you the traffic ticket of...

HHow do i go about my ticket? The ticket that I got is all screwed up

Need more information about the ticket to answer. Perhaps reach out to an attorney who can probably go to court instead of you and probably get you...

Will an NYC DMV extradite me to NJ for misdemeanor contempt of court charges?

I do not think the DMV detains people for warrants. If you are suspended in NJ you won't be able to get a NY license even if you never had a NJ...

Is there a time frame for sending out these red light tickets?

It may be somewhat delayed but not something that would invalidate the ticket.