Is the Fatihah recited only in the third and fourth rak'ahs of the Sunnah prayer before Dhuhr, or does the Sunnah prayer differ in this regard?

It is preferable to perform the pre- and post-Dhuhr regular (Sunnah) prayers two rak'ahs by two rak'ahs. However, it is permissible to pray them as four rak'ahs with a single taslim. It is also permissible to recite a surah after Al-Fatiha in the third and fourth rak'ahs, or to suffice with Al-Fatiha only.