Short answers, pulled from the story.
Most Latin nouns have five cases: nominative, accusative, genitive, dative, and ablative. Nouns for people add a sixth case, the vocative, used for direct address. A seventh case, the locative, survives only in names of cities and small islands, and in words like domus ("home"), as in Romae ("in Rome") and domi ("at home").
Latin verbs can take more than a hundred different endings to express different meanings. These endings convey person, number, tense, aspect, voice, and mood, sometimes combining with participles and parts of the verb sum ("I am") to form periphrastic tenses.
Latin nouns fall into five declensions, each grouped by the pattern of their case endings. First-declension nouns typically end in -a in the nominative singular and are usually feminine (e.g., puella, "girl"). Second-declension nouns in -us are usually masculine (e.g., dominus, "lord"). Third-declension nouns vary in form and can be any gender. Fourth and fifth declensions are less common.
Latin word order is flexible because grammatical function is carried by inflectional endings, not by position in the sentence. A noun's role as subject or object is shown by its case ending, so the same words can be rearranged for emphasis or poetic effect without changing the core meaning. Poets such as Virgil exploited this freedom for both rhetorical and metrical purposes.
Deponent verbs are Latin verbs that have the form of passive verbs but carry an active meaning. The verb sequor, for example, means "I follow" despite looking passive. They are considered relics of an older mediopassive voice that Latin once possessed.
The number 1,000 in Latin is mille, an indeclinable adjective, so "I saw a thousand lions" is mille leones vidi. Multiples of 1,000 work differently: milia becomes a neuter plural noun followed by a partitive genitive, so "I saw three thousand lions" is tria milia leonum, literally "three thousands of lions".