"Our house has three windows."
Translation:हमारे घर में तीन खिड़कियाँ हैं।
It is in the oblique case. This is when the noun phrase (हमारा घर) is the object of a postposition (in this case में). हमारा becomes हमारे in the oblique case.
No. हमें is used in the accusative and dative cases and is equivalent to 'to us' or 'for us' (instances where you would use को for nouns). हमारा/हमारी/हमारे is equivalent to 'our' and used in the genitive case to denote relationships and possessions (where you would use का/की/के for nouns).