If dating includes sex (or any form of sexual activity) then the answer is NO - and parental approval is irrelevant. If you are under 16 then you may not lawfully engage in any sexual activity (not just intercourse) with anyone.
Is it bad for a 13 year old to date a 16 year old?
The question as phrased, the answer is no. It is not legal. If the 16 year old engages in any sexual conduct with the 13 year old, they could face statutory rape charges and the parental consent assuming there was any would have no bearing
Can a 15-year-old girl date a 17 year old boy?
The critical law to understanding the gravity of the danger is to understand that a person under 18, under California law, cannot legally consent to sexual conduct (Penal Code § 261.5(a) (defining minor)). “Dating” can certainly imply sexual contact, which is illegal between a fifteen-year-old and an eighteen-year-old.