Does a student's forgetting everything in an exam permit him to ask a friend about the beginning of an answer, knowing that this might help him remember the rest of the lesson, and is this considered cheating? And is it permissible for a student to answer questions in an exam that include events about alcohol or Christianity?

Yes, forgetfulness is considered an excuse, but it does not justify seeking help from a friend during an exam. The Permanent Committee for Issuing Fatwas was asked about a student helping a colleague in an exam due to forgetfulness, and they replied that this is forbidden cheating, based on the hadith "Whoever cheats us is not of us," and due to its danger to education and society. As for the second question, the answer is that there is no harm in answering the curriculum material in an exam, because no evil or falsehood results from the answer sheets.