Compared to Proto-Indoeuropean, ancient Germanic languages were down to 4 cases (nominative, accusative, dative and genitive), plus traces of a fifth one (instrumental). In Latin and Greek a few more cases survived. The similarities in the declensions among different Indoeuropean languages are relatively easy to spot though.
Finnish has plenty of cases, but they're very different from Indoeuropean cases. They work a lot like postpositions. That's the thing with agglutinative languages.
As for the Old English stuff...
Good job introducing the basic grammar concepts, Leodfriþ! For some reason, English-speaking countries don’t seem to teach this kind of stuff at school and only students who get into linguistics-related degrees at uni get a proper dose of basic grammar. In Spain we put a lot of emphasis into morphosyntactical parsing, and we learned some Latin, so fortunately I never found Old English grammar intimidating.
Now! Corrections!
It is what is in modern English a passive sentence. Instead of "the dragon slew the man" it is now "the dragon was slain by the man", in modern grammar.
This is a bit of a stretch. Your first translation, “It was the dragon that the man slew”, is closer to the original. Moving an element to the opening position in a sentence is known as
topicalization, and it merely adds emphasis to the topicalized element. Modern English has lost many its capabilities in this regard, but it still retains a few similar constructions, while topicalization is usually expressed by intonation rather than by word order: “The man slew THE dragon” would be an option. Modern German for example uses topicalization extensively.
Dative: Indirect possesive - for example "your people". Not directly his people as though they are his assets, but they are of his kind therefore indirect possession.
The dative was used in expressions that are better translated with a possessive in Modern English (for example,
7 mearcode him on heafde halig rode tacen, literally “and [he] marked him on [the] head [with the] holy sign of [the] cross”, would be translated as “and he marked his head with the holy sign of the cross”). But that was an idiomatic, secondary use of the dative. Its main function was to express the indirect object. This, in the sentence “I give you the horse”, “I” is the subject, “the horse” is the direct object and “you” is the indirect object – in Old English, it would be “ic (subject, nominative) þe (indirect object, dative) gife þæt hors (direct object, accusative)”.
Of course, that’s simplifying things. The main function of the dative, after all, was as a prepositional case – i.e. it was the case a word governed by certain prepositions had to be in. But this is better left for a more advanced lesson.