Will I have the opportunity to plead not guilty and obtain a lawyer for a speeding ticket and charged w/operating w/out license?

Contact a local traffic ticket attorney. The fee is up to each individual attorney. Call around and see who you feel most comfortable with but...

Ive gotten a ticket for no insurance but had insurance in 2015 what do i do?

Show all your docs to a local traffic ticket attorney.

Does a mistake on a Traffic ticket invalidate the ticket?

May help you win the case but does not invalidate the ticket.

How do I handle two out of state driving with out a license tickets?

You would not have to appear in New York if you retain an attorney to go to court instead of you.

My driver license will be suspended due to falilure to appear for hearing?

Most likely the letter went out before the attorney rescheduled the case. This is typical.

The fine is up the judge, from $90 to $300 with a $93 surcharge. You're also facing a $300 Driver Assessment Fee. In NY an attorney can typically...

It is valid. A local traffic ticket attorney probably gives you the best chance at beating the ticket and your attorney can go do court instead of...

According to the NYC DOT all motorcycles are permitted in all HOV lanes. http://www.nyc.gov/html/dot/html/motorist/carpool.shtml

In New York State can I get ticketed for letting an unlicensed driver drive my vehicle

Unlicensed no but suspended yes, though ticketed very rarely.

What happens if I avoid being served traffic citations by a police officer?

The tickets are not valid unless they are personally served upon you.