"He" and "she" essentially act as normal nouns here, instead of pronouns. You can't say "the he or the she". Consider the following example to understand why: "Bill lives across the street. He's a pilot now." - You say "a pilot" because while you've mentioned "Bill", you haven't mentioned "pilot". If you said "Bill lives across the street. He's the pilot now" the listener would think "Wait.... when were we talking about a pilot? I mustn't have been paying attention." If you were talking about a pilot, and a few minutes later said "He's the pilot", the listener would know that Bill is the pilot you were talking about. If you were talking about a pilot and later said "He's a pilot", the listener would know that there are two different pilots. You wouldn't say "the he or the she" for the same reason. If someone told you they had a baby and you said "Is it the he?", the listener would be confused as to who "the he" is. "It" obviously refers to the baby, but "the" implies that the baby is also someone else ("a he") who you were previously talking about. But you could never say "the he" in any context because, as a pronoun, "he" should never have an article in front of it. "A he" is technically also wrong, but asking if a baby is "a he or a she" has become common in colloquial language. It's wrong, but it's still used informally. Here's a really simple way simple way to understand articles: "the" is simply the adjective form of "it". It has the exact same function in a sentence, but instead of replacing a noun it appears in front of it. If you said "I have a cat. It is fat.", "it" obviously refers to the cat. But if you said "I have a cat and a dog. It is fat", the listener has no idea if "it" refers to the cat or dog. If you said instead "I have a cat and a dog. The cat is fat.", it's obvious that the cat you have is fat. If you said "I have a cat and a dog. A cat is fat", there are two cats: one you have, and another somewhere on Earth that is fat.

I would say, "is it a he or she?" But I will usually use, "is it a boy or girl?" Or even, "is it a man or woman?" Actually I sometimes use slang like, "is it a dude or a chick?" But honestly all the above will work.

As for the second question I don't know too much about all the complex rules of the English language but as a native speaker all I can say is, "it just doesn't sound right." But that is a good question though never really thought about it before.