"The professor's pen is brown."
Translation:قَلَم اَلْأُسْتاذة بُنِّيّ.
Is it right to assume, that the case endings should be something like: "قَلَمٌ الأُستاذةِ بُنّيٌّ" with a kasrah added to "الأُستاذة" because it's in genitive case?
Yes, it is. Here, الأُستاذةِ is in genitive case because it refers to the possessor of قَلَمُ.
However, the word قَلَم shouldn't be with /tanwin/ because it's defined by annexation, so the case ending should be "قَلَمُ الأُستاذةِ بُنّيٌّ"