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.

1110a violation?

Definitely . If you were avoiding a hazard you have a proper defense.

Will I lose my license?

Free legal advice: Do not under any circumstances plead guilty to the second ticket.

How does this work?

Attorneys do not know for sure. Perhaps call your insurance company.

traffic ticket for 1110A/Disobey/ do not enter

Reach out to a local traffic ticket attorney that is familiar with Manhattan tickets. This probably gives you the best chance at getting the ticket...