Q. 1. "What is a conditional baptism?"
A. 1. A "conditional baptism" is a "Christian baptism administered when there is doubt whether a person has already been baptized or whether a former baptism is valid."
Because there is doubt as to the validity of the first baptism, the person is baptised conditionally. If the first baptism was valid, the second one is not valid. This is because a person can only be baptised once. If the first baptism was not valid (not properly administered), than the second one is the valid one.
Conditonal baptism are performed when there is an uncertainty as if a person was previously baptised, or properly baptised. While it is done in many cases when someone converts from another religion, it is not automatically done. There has to be a reasonable doubt and serious investigation of the previous baptism.(Rite of Reception of Baptized Christians into Full Communion with the Catholic Church, no. 480, and 1993 Vatican Directory on Ecumenism, nos. 94-95 and Code of Canon law, # 845).