I have some undergraduate training in linguistics, though I wouldn't attribute much grammar knowledge to that. It does come in when you see me complaining that there's no semantic distinction between direct and indirect objects.

I've always been interested in language, so I am likely to pick things up and remember them.

You get fun facts about Latin and Mandarin because those are the languages I have studied. If you want to have examples available of how different languages work and how different categories might or might not be realized in different languages, there's not really a substitute for learning different languages.†

Studying Latin in particular is likely to familiarize you with a lot of English grammatical terminology, much of which was developed for the purpose of discussing Latin grammar. Latin's grammatical structures can be very explicit compared to English or Chinese (where the grammatical structure is of course still present, but it's more difficult to point at something concrete in the sentence and say "_this_ element of the sentence reflects _this_ grammatical feature!")

† Another example of what you might consider edge cases in the space of transitive/intransitive verbs or direct/indirect objects: in Latin, dono is a "ditransitive" verb, which is to say that it may take two direct objects, defined appropriately for Latin as objects which appear in the accusative case. This is pretty unusual. The two direct objects of dono (source of the English verb donate) are a gift and a recipient.

Latin has a much more common giving-related verb, do, which means "give". It is obviously possible to supply a gift and a recipient to do, but for this verb the gift is a direct object and the recipient is an indirect object. (In fact, this verb is the source of the dative case's name!)

So far these are just fun facts about Latin. But if you draw analogies to English, you find something interesting: once we define English direct objects as unmarked and indirect objects as marked by a preposition, we find that most English verbs accepting an indirect object may be regularly transformed into ditransitive verbs. "He bought a dress for his wife" and "he bought his wife a dress" are exactly equivalent statements. Here, some additional structure is provided by the ironclad English requirement that the first object in "ditransitive form" must correspond to the indirect object in "transitive form", and it's common to just call the first of the ditransitive objects an indirect object.

This might lead us to think that "ditransitive" doesn't really make sense as a separate class of verbs in English, but that's not quite true either; there are certain verbs, like bet, which can accept multiple direct objects none of which may appear as indirect objects instead. ("Bet [you] [four dollars] they won't.")

I believe that either object of an English verb in ditransitive form may be promoted to the subject of a passive form of the verb. That would be good evidence that it is really a direct object, except that in English the prepositionally-marked indirect objects of verbs may also be promoted to the subject of a passive form of the verb ("The baby wants to be sung to").