Can we read the same surah in all rakats of salat? Eg. If I read "Surah Kosar" in Farz, can I read it again in Sunnah r nawafil or not.
There is nothing wrong in doing such. And there is nothing preventing one from doing that. It is narrated in Saheeh Bukari of an Imam who used to recite a surah and another one with it in each Rak'ah. Furthermore that Fard, Sunan, and Tatawu' salat are different prayers, you may read surat Al Fatihah and any surat you wish in each of them. Allah A'lam, May Allah guide us all.