Translation:Of the speech
2)Correct-ish (Who does "him" refer to? The owner himself or somebody else?). It's better to avoid two genitives in a row, so the better choice is: "Αυτός δεν αρέσει στον σκύλο του ανθρώπου" -or (depends on the intended meaning)- "Ο άνθρωπος δεν αρέσει στον σκύλο/του σκύλου."
3)Either is correct ("γάτος/γάτα"). If the cat's gender is unknown, use the female noun.
The Greek sentence doesn't have a preposition either, so it could be either "... dem Gespräch" or "... des Gespräches", depending on context. Modern Greek has lost the Dative case, so it uses either the Accusative or Genitive where German might use the Dative case.