The magic Apple Support:

A few days ago, I suddenly couldn't login to iCloud on my mac. I thought it was something that would be gone if I would try turning it back off and on again. Didn't work. Used the mac without bothering about it. I was too lazy to call the Apple Support and it didn't annoy me that much.
A day later, suddenly Spark (my email client) didnt work either, it asked me all the time to re-login into one of the accounts but "an authentication error occured". At that point I thought it was a problem with the keychain. Because i don't use email that often and the last time I should pay 30€ if I wanted to call Support (out of warranty), I just started using email on my phone.
Yesterday, MS Office (yes I use it and I like this Microsoft Product and I'm an Apple fanboy) wouldn't login either. I didn't call them.
Today, I had finally time to call them. They didn't want to charge me since I selected an Apple-Id Problem (and I think the Support Hotlines are free to call idk). The call from Ireland came 2 times and the connection didn't work (thanks iPhone). The third time, the moment the Support guy said Hello iCloud worked. A few second later Office and Spark worked again too. I don't know how these coincidences happen. Anyway, I am just happy my stuff works again and I don't have to use Google Docs and write my mails on my phone.