What is the general rule concerning the Sunnah prayer before the obligatory Dhuhr prayer? And is there a general rule concerning the supererogatory (Nafl) prayers? And is the saying: "The Sunnah prayer should not resemble the obligatory prayer" correct?

The rule that Sunnah (supererogatory prayer) does not resemble Fard (obligatory prayer) has no evidence supporting it. For example, the Fajr prayer (both its Sunnah and Fard) consists of two rak'ahs, and the only distinction between them is the intention. The prohibition against making Witr prayer resemble Maghrib prayer was mentioned in the context of a specific supererogatory prayer resembling a specific obligatory prayer, and it is not a general rule. Some meticulous scholars have chosen the interpretation that the meaning of the prohibition against making Witr resemble Maghrib is that one should pray Witr three rak'ahs connected with two tashahhud (recitations of testimony), and it is permissible to pray it three rak'ahs connected with one tashahhud, as the resemblance is absent in this case.