Sentence not making sense (oblique case)?
For some sentences, I do not understand why the noun has not changed for the oblique case. For example,
उनके पिता भारत में रहते हैं - Why isn't पिता changed to पिते?
उनका घर अमेरिका में है - I thought it was supposed to be उनके for the oblique case?
उनके घर अमेरिका में हैं - Doesn't घर have to change to घरों since the postposition 'में' is referring to घर?
किताबें मेरे घर की हैं - Which one is the noun that has to be changed (the one the postposition is referring to and the oblique case is applied to). Why isn't it किताबों?
If anyone could help me with this, it would be great.
Only the object of the postposition changes to oblique case. In उनके पिता भारत में रहते हैं, the object of 'में' is 'भारत'. Essentially, the object of में is the noun/noun-phrase that answers the question किस में (in what) and occurs just before the postposition.
The object of में in both उनका घर अमेरिका में है and उनके घर अमेरिका में हैं is 'अमेरिका'. So, उनका or घर does not have to be in the oblique case.
In किताबें मेरे घर की हैं, the object of की is 'मेरे घर' becauase that is the answer to the question 'किस की'. This is why मेरे is in the oblique case form. किताबें is not the object of the postposition so it's in direct case.
Note: In your first sentence पिता was in direct case. But even if it were in the oblique case, पिता and other masculine nouns referring to people like मामा, राजा etc are the exception to the rule that masculine nouns ending in ा change to े in the oblque case. They retain their forms in the oblique case. I'm not sure why that is but I suspect it has something to do with the use of respectful pluralization with these words. For example - यह मेरे पिता का बटुआ है - 'This is my father's wallet' (पिता doesn't change to पिते).