If you are angry, consider delaying the response for a few hours. It is remarkable how much you may want to change what you say after that time. If there are less than 10 questions in an email, consider responding to all of them. You do not have to answer them and may not wish to if they are enquiring about something personal. Avoiding tricky questions can be seen as an admission of having a weak position.
Dubious assertions seem reasonable in the light of incomplete evidence.
Keep all the emails in a discussion and remember all the questions so that they need not be asked more than once. Be prepared to look at webpages that are suggested. Think carefully before making an argument with which you are not comfortable. Consider reading books especially if they are in a new area. If someone is behaving in a childish way, it is better not to comment.