umm i think he's around 18-19.. the whole timeline is confusing because we read that wooyoung just graduated highschool and is doing college abroad, so his childishness is kinda understandable. he's still a kid and is bound to act like one even with a child. i understand why you might find his childishness annoying (i sometimes do too) but you can't tell someone who just became an adult and was spoiled all his life to act mature. and kyungjoo is wayyy older than wooyoung (i think he's like 30 because he's around the same year as wooyoung's brother and the brother's age gap is 9 years). so im sure kyungjoo knows what he signed up for when he got into a relationship with someone much younger than him.
Wooyoung is so childish, it's hard to like him. He's 22(?) but acts like he's 14. Sometimes, it amusing but it gets old real fast. Even though i get why Kyungjoo likes him, I actually feel bad for Kyungjoo that he has to deal with someone so temperamental and spoiled.