Kids ride only with adults, not sale tickets for children travel alone. But check the official page of BART for rules.
There are no single ride children tickets on BART. Children 4 and under ride free but everyone else must have a valid BART ticket or Clipper card. For the Cable Car SFMTA will accept Cash or Clipper. Clipper discount cards for youth and other details see the BART tickets pages (https://www.bart.gov/tickets) and SFMTA (https://www.sfmta.com/fares/cable-car-single-ride)
I have no idea. Didn't even know there's such a thing as a child ticket. I am guessing you are referring to tickets for the cable cars.
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