You can book a cab via following methods:
Online: http://www.li-yellowcab.com
Telephone: +15162491212
Email: sales@longislandyellowpages.com
Yes, it's possible to pre-book a cab with Li Yellow Cab, please contact the company.
Li Yellow Cab has both regular and air-conditioned cabs, please mention your preference at the time of booking.
Please contact the company on their helpline number to make any changes.
Generally drivers will meet the passengers at the arrivals on airport pick ups but do check with the company.