Why is "They enter to those schools" not acceptable? In meaning "come into"
No you cannot say "enter to". In English, "enter" normally takes a direct object in this context and no preposition is required, i.e. you cannot "enter to" something. However there are some contexts in which you can say "enter into" but that does not apply here as the context and the meaning would be quite different:
There are unexplained elements here. They must be guessed at by the learner, so...
I'm guessing that "ke" indicates some directionality and, perhaps, must be used with the verb "masuk"?
I'm guessing that although "itu" means "those," here it is functioning the create the definite article ("the")?
you are right, "ke" is more like "to" in english
Since indonesian doesn't really have translation for the Article, you are right again, "itu" here is used to translate the "the", or depending on the context, we can also use "nya" eg. "sekolahnya"