What type of illness that permits breaking the fast in Ramadan?
It is an illness that, if one fasts, there is a fear it may lead to their death or cause unbearable hardship.
Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.
What is the ruling on someone who curses the religion or commits an act of disbelief during the day in Ramadan?
Whoever apostatizes (leaves Islam) while fasting, their fast is invalid. Cursing the religion is an act of apostasy (may Allah protect us from it). Such a person must return to Islam by pronouncing the Shahadah (testimony of faith), seek Allah’s forgiveness, refrain from eating and drinking for the rest of the day, and make up for that day’s fast later.
What is the ruling on wiping the white area behind the ears instead of wiping the head?
The obligation in ablution is to wipe some of the head; it is not a condition to wipe all of it. Wiping the white area behind the ears suffices for that. And Allah the almighty knows best.