The Hebrew word is na'ar. It is used of Isaac who was 28, Joseph who was 30, and Rehoboam who was 40. God took the taunting of these children in Second Kings personally in this way. Though Elijah was bald, he lived another 50 years, so he was probably prematurely bald. However, the "Go up" of verse 23 was the real taunt and was blasphemous about the way that God was intending to raise Elijah to heaven. It was a blasphemous insult to God. These children were certainly old enough to have been taught the scripture and respect - especially respect of God. In verse 24, the Hebrew word for children is a different Hebrew word and actually refers to/means progeny - the produce of the womb. My children are 38 and 40. They are still, and always will be, my progeny. In a couple of places in the scriptures (one in Psalms) God says, "Touch not mine anointed, nor do my prophet any harm." Today, there is virtually no respect for pastors/ministers. Most of that is due to some of the ones who have acted in unholy ways, to be sure, some is due to lack of teaching true respect in the home. But it really makes it hard for the ones who try to follow God, hear Him and love others. What if God did the same in this dispensation as He did in Second Kings? Would it help to bring back respect for these men/women of God? Fortunately for us, this is the age of Grace and not Law!
Question two - Could this be mistranslated? It is a poor translation. The problem with translation is that languages and words change in meaning. Example: the Gay 90s and gays today. In the King James times, you would have a sentence like this. "Bring the carriages freely by and by." We would not understand that today without a little research. Carriages were pieces of luggage, freely meant without pay, and by and by meant immediately. (Does that make you scratch your head?) So the sentence today is "Bring the luggage immediately without pay." The problem all translators have is how to stay true to the original language and yet still express the truth in modern parlance.
Paul's exhortation to Timothy is still relevant today. "Study to show yourself approved unto God, a workman that does not need to be ashamed, handling correctly the Word of God." (2 Timothy 3:15)