Legally, what berkeley, california police based legal standard for walking bicycle in the residential neighborhood street? Walking with the bicycle at the side, and, or, walking while bicycle is underneath, and, or straddling the bicycle, with both feet on the ground while walking with it? Please define clearly, with website references, videos, and, or, graphics, please?
You were probably fined under the California Vehicle Code 21113(f) which doesn't specify what you're asking.
However, this is not the final source and I am still waiting to hear whether this happened on campus grounds, or in a commercial city zone, because I don't remember seeing these signs in any "residential area neighborhood" in Berkeley.
(f) A transit development board may adopt ordinances, rules, or regulations to restrict, or specify the conditions for, the use of bicycles, motorized bicycles, electric bicycles, skateboards, electrically motorized boards, and roller skates on property under the control of, or any portion of property used by, the board.
(g) A public agency, including, but not limited to, the Regents of the University of California and the Trustees of the California State University, may adopt rules or regulations to restrict, or specify the conditions for, the use of bicycles, motorized bicycles, electric bicycles, skateboards, electrically motorized boards, and roller skates on public property under the jurisdiction of that agency.
(h) "Housing authority," for the purposes of this section, means a housing authority located within a county with a population of over 6,000,000 people, and any other housing authority that complies with the requirements of this section.
(i) "Public transportation agency," for purposes of this section, means a public agency that provides public transportation as defined in paragraph (1) of subdivision (f) of Section 1 of Article XIX A of the California Constitution.
http://www.calbike.org/bicycling_in_california_sharing_the_road In Berkeley you may ride anywhere, except certain prohibited areas or where you would impede the flow of traffic, each city in CA has different rules on sidewalks that vary and are can apply to only certain sidewalks or all, or a mix. You can walk a bike in each ways you described except places like interstate highways where you can't walk. Warning: laws being what they may, you could run into a cop who doesn't care, is ignorant of the law, or is simply a sociopath that enjoys ruining your day.