Going on dates isnt per se illegal, but at your age, there are a large number of things that ARE illegal and could lead to him facing felony charges, even if hes only charged as a juvenile.
Can a 13 and 16 year old date?
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
What age should Teenager date?
According to the American Academy of Pediatrics, kids start dating at an average age of 12 and a half for girls and 13 and a half for boys. Every teen — or preteen — is different, though, and your child might be ready sooner or later than their peers.