Ferdinand and Isabella were second cousins and their marriage united Spain. When they married they got the title of “Catholic King and Queen” this title was given to them by Pope Alexander VI in 1494 because of their defense of Catholicism inside their realms. - This makes number 1 correct.
Because of the title, their reign was characterized by religious unification. This is the reason the Inquisition began in Castile. The pope gave Ferdinand and Isabella full power to name inquisitors - the reason that numbers 2 and 3 are correct. Their reign was in favor of Rome and this is the reason the Pope gave them enormous power inside the Spanish Inquisition.
This is the reason number 4 is incorrect because there was never a war between Rome and Spain, the Inquisition was something that Ferdinand and Isabella both wanted to maintain their power in their realm and they got authorization from the Pope to do so.