The European Schools are an intergovernmental institution separate from the EU. If the United Kingdom left the EU this would not necessarily mean withdrawal from the European School system. Politically it is feared that the British government would also pull out of the ES since, in the negotiations on the current financial framework, it demanded the closure of these schools.
European school Luxembourg 2 is also regularly checking children email communication and they punish them if they find inappropriate words or content. Children are sending emails between each other so anybody who reads this kind of emails should have explicit written permission from the account owner