This odyssey came to an end. Today I received an answer and a shipping notification.
Meanwhile I assume that a plus sign in the email address (something+foo@…) is an issue for some parts of Banggood’s system. It works fine for registration, sending emails etc. but fails in a particular step in the order process. Google understands this format as an email alias address. I use a different alias for every site so that I can trace back leaked email addresses (and block unwanted mails easily).