"This car is mine."
Translation:यह गाड़ी मेरी है।
इस is the oblique form of यह and उस is the oblique form of वह. So, you use इस/उस only when it is followed by a postposition (like में, से, पर etc) and यह/वह otherwise.
'इस घर मेरा है।' is incorrect. 'This house is mine' should be 'यह घर मेरा है', similar to यह गाड़ी मेरी है।
However, if you want to say something like 'There is a ghost in this house', you would say 'इस घर में भूत है'. Because of the postposition में, इस is in the oblique case.
'यह कमरा मेरा है' is a correct translation for 'This room is mine'.
'यह मेरा कमरा है' would translate to 'This is my room' instead of the required sentence. Don't know why duo would suggest that... Similarly, 'यह मेरी गाड़ी है' would translate to 'This is my car', which is again not the required translation.