"I know her family."
Translation:Conosco la sua famiglia.
No, "sapere" is used for knowing information, "conoscere" for being acquainted with people.
You don't need it with the names of the relatives next of kin (in singular form) when combined with posessive pronouns: mia madre, mio padre, tua sorella, vostro fratello, nostro zio, tua zia, etc. (exceptions: LA tua mamma and IL tuo babbo). But you need an article: 1) when using plural form: "le mie sorelle" (my sisters). 2) when there's an attribute adjective: "il mio fratello minore" (my younger brother), "il mio caro cugino" (my dear cousin). 3) when using diminutive suffixes: "il mio fratellino", "la mia sorellina". 4) the pronoun "loro" always requires an article: "la loro madre" (their mother), "il loro fratello" (their brother).