Why 'mere'? Should not it be 'mera' or 'meri' ?
Due to का - i.e. subject is brother's house, not he himself.
Is बूढ़ा and पुराना used in the same way?
बूढ़ा is usually used for people. पुराना is usually used for objects.
It doesn't accept "my brother's house is really old."
If this is in the oblique case (bc of का) then why is it पुराना instead of पुराने?
पुराना is describing the house, which is not in the oblique case.
There is no 'this is in the oblique case', if 'this' refers to the entire sentence: nouns have case, and their adjectives agree with them.