Yes, it's a case (as "complemento di termine") of the personal pronoun and the same as "a lui", "ad esso"; it's commonplace as "ad essi" too (originally "loro"), and incorrectly common as "a lei" (correct "le"). Incidentally, these pronouns become enclitic in some conjugations (e.g. imperative "leggigli" (you read (to) him ...) or infinitive "leggergli" (to read (to) him).
Esso is the equivalent of "it" in Italian, and "essi" is the traditional "they"; they're disused in modern speech, but you'll find them in literature. There is no other subject pronoun to mean "it", though.
As for correctness, "Gli leggo un giornale" or "Leggo un giornale a lui" is supposed to mean "I read him a newspaper", and "Leggo loro un giornale" or "Leggo un giornale a loro" means "I read them a newspaper"; however, grammarians have long come to accept that "Gli leggo un giornale" could mean "I read them a newspaper" too, so that isn't wrong either, although it adds confusion.
Enclitic and proclitic are the two forms a clitic (non-stressed particle) can assume in grammar: in "gli leggo" gli is proclitic, because it's pronounced together with the following word; in "leggergli" gli is enclitic, because it's pronounced together with the preceding word (leggere), and in Italian spelling as you can see it's attached as a suffix.
No, "loro" is not clitic, so it doesn't follow this rule, and instead when used as an indirect object pronoun it usually goes after the verb. It's also rather "exceptional" as a possessive pronoun, as it's the only one to always require an article, but it's probably too soon to write about that.
The clitic form of pronouns always has to precede the verb (the auxiliary in case of composed tenses); there is also a fixed word order when there are two clitics, as the indirect has to precede the direct, and they sometimes are merged into a new form (e.g. "glielo" = "gli+lo" = "it/him to it/him").
As others said, "GLI" here is not the definite article for masculine plural (as in GLI amici = THE friends) but stands for an indirect object (GLI --> A LUI --> to him). Unfortunately in current Italian it is also used (quite usually) to mean A LORO --> to them and, incorrectly, A LEI --> to her (which should, really, be "LE"). In spoken Italian you will then hear "GLI leggo un libro" (which normally means "I read HIM a book") to mean, instead, "I read HER a book"). The correct form for "LE leggo un libro" should be "I read HER a book". See also the explanation of f.formica. HTH :)