Actually, Prime Video and Amazon Music Unlimited are widely available in Europe:

https://www.primevideo.com/ (worldwide)

https://music.video.com/ (several dozen countries, including Finland, Sweden, Poland, Portugal, Bulgaria)

As for retail, Amazon Germany (https://www.amazon.de/) offers English language and free shipping to ~10 European countries, including Sweden and Finland. Belgium, Netherlands and Luxembourg get Prime shipping benefits.

The implementation still leaves a lot to be desired, though - e.g. there is a lot of untranslated content (German reviews, for example).