On account.adobe.com, my ID and password work well. As I tried to register on ADE, I got an error that says "ID/password wrong. ebook provider wrong. Try again.". As an ID, I tried full email and just the name. I also haven´t got an email with a verification of registration. But as account.adobe.com works.. I guess, this wouldn´t be necessary.
What do I do now?
You don´t have password problems online, but with the ADE login. Take care you do not use german Umlaut letter (ä, ö, ü) or special characters. After changing the password, ADE login worked fine.