Is it obligatory to make up for prayers whose performance is doubtful after more than three months have passed, or is it also obligatory to make up for all prayers performed during this period?

Scholars differed concerning one who doubts having performed a prayer after its time has elapsed, as to whether it is obligatory for him to make it up. The relied-upon view among the Hanbalis is the obligation to make it up, because the default is that he has not performed it. Abu Hanifa holds that making it up is not obligatory.

Making up the three prayers mentioned in the question is more cautious and more absolving for one's conscience. There is no need to make up any others, because the order among prayers is recommended according to many scholars, and the order is waived by forgetfulness, or by the worshiper believing that he has no prayer due except the present one he is performing.