Meaning of infinite self inductance
If self inductance is infinite, then any rate of change of flux would generate infinite voltage, but look at it the other way. Any amount of back emf can be generated with infinitesimally small rate of change of flux. When we apply a voltage to the primary of a transformer (with no secondary load), an equal and opposite back emf is initially generated and no current flows. In order to maintain the back emf, there must be a rate of change of flux, which requires an increasing primary current. The larger the self inductance, the smaller the rate of current rise  required to maintain the emf. As self inductance approaches infinity the rate of rise of current approaches zero. So in the ideal transformer one could apply a voltage to the primary for ever with no current flow. The voltage across the socondary will be the primary voltage times the turns ratio. The current in the primary will be the secondary current / turns ratio.