Lots to unpack here, but this is a decent summary:
https://www.state.nj.us/transportation/commuter/bike/regulations.shtm
Answers to most of your questions re: responsibilities as they pertain to a cycling *being passed* are here (I find if comical that they missed #5 in the Operating Regs section btw):
39:4-14.1 Rights and Duties of Persons on Bicycles.
Every person riding a bicycle on a roadway is granted all the rights and subject to all of the duties of the motor vehicle driver.
39:4-14.2, 39:4-10.11 Operating Regulations.
Every person riding a bicycle on a roadway shall ride as near to the right roadside as practicable exercising due care when passing a standing vehicle or one proceeding in the same direction. A bicyclist may move left under any of the following conditions: 1) To make a left turn from a left turn lane or pocket; 2) To avoid debris, drains, or other hazardous conditions on the right; 3) To pass a slower moving vehicle; 4) To occupy any available lane when traveling at the same speed as other traffic; 6) To travel no more than two abreast when traffic is not impeded, but otherwise ride in single file. Every person riding a bicycle shall ride in the same direction as vehicular traffic. In New Jersey, the law states a bicyclist must obey all state and local automobile driving laws. A parent may be held responsible for the child’s violation of any traffic law.