FAA Regulation

Visual observer. Person manipulating the controls. Remote Pilot in Command (Remote PIC). 

12 hours. 8 hours. 24 hours.

Remote Pilot in Command. Commercial Balloon pilot. Designated Pilot Examiner.

600 feet AGL. 500 feet AGL. 400 feet AGL.

They can maintain line of sight and without loss of control.  They briefed each other before the flight. They are in radio contact the entire time.

is operated by a Part 61 certified pilot. documents maintenance, preventive maintenance, alterations, and inspections.  is only operated over small groups of people.

must not cause injury equivalent to 25 foot-pounds of kinetic energy upon impact. be operated in accordance with the operating limitations specified in the approved Flight Manual. be 0.55 pounds or ...

No, the other people in the park are not on notice.  Yes, as long as the park is not busy enough that it would be considered an open-air assembly of human beings.