I ride my bicycle in Brooklyn on a street where there was a bike lane. Am I bound to follows the laws applicable to a car or other motor vehicle?

Yes. The New York State Vehicle and Traffic Law (VTL Section 1231) expressly provides that “every person riding a bicycle…. upon a roadway shall be granted all of the rights and shall be subject to all of the duties applicable to the driver of a vehicle….” Obviously, there are some special rules that apply to bicycles and to such extent you are treated differently than a car which has its own applicable rules.  Bicyclists and all motorists are mandated by law to obey the statutes and rules governing the operation of such vehicles and most importantly are entitled by law to assume that other drivers will follow such laws as well.