There is no two valid Talaq together. Valid Talaq with all its conditions including declaring it in front of two Aadil ( Pious) witnesses, counts just one Talaq. There is no second Talaq immediately after it. Second Talaq can only be declared if the marriage is reinstated again, then all conditions of Talaq were accomplished. .
Iddah period after valid Talaq is three menstrual periods, and if the woman has no regular period, then it is three months.