I think you already know the possessive marker: John's, Mary's, the government's, our car's
Past participles can end in -ed, like past-tense verbs, but in some cases they end in -en: "had given," "had gotten," "had stolen," "had spoken," "had written." Some -ed examples: "had called," "had walked," "had talked."
The examples you wrote down are all correct, except that "laughing" shouldn't have a T. (There's a T in the noun "laughter," but not in verb forms of the word "laugh.")