Case 1: adhan called for Dhuhr before its entry is not treated as the prescribed time-announcing adhan under the general Hanafi rule.
Case 2: adhan without wudu is valid, though wudu was preferable.
Case 3: for two consecutive missed prayers, both calls for the first and iqamah alone for the second are permitted.
Case 4: omitting the Fajr addition is a defect in a specific Sunnah expression, not the same as omitting the whole call.