"Do you respect her?"
Translation:Vážíš si jí?
Yes, cases work differently in different languages. There's also a different number of cases in Czech than in German. And there is really no way to figure out why "vážit si" (to respect) or "bát se" (to be afraid of) or "dotýkat se" (to touch) or several other verbs need the genitive. You should learn the required case (together with any reflexive pronouns and prepositions) together with each verb.