I will replace my actual smartphone with a new device due to a broken display. Is there a chance to reinstall Kurviger Pro on my new device without having to repay 10 Euros for new - or do I have to repay ( which would be bad to be honest ) ?
“You can use apps you bought on Google Play on any Android device without paying again. However, each device must have the same Google Account on it.”
Can see here the official Google Play Help and how they organized the Android ecosystem.
That is good news - thanks for your feedback ! 
Merci und Grüße,
Stefan