Do I have to validate a single form field? Not necessarily. The article was written to show the simplest use case. You could also do validation based on any combination of form data. You should not consider this solution limited to input text fields as well.
Should I use XML or text for the responses? If you do keep in mind the server resources that will be used to parse and generate the XML. Simple validation could be done with a simple text string. If you want to provide more information consider using JSON.
What issues do you face using AJAX to validate form data?