I will try and help but other may be able to elaborate some what.
Some of what I say is purely assumption but may well give you a basis on which to research.
1) get a VISA for your destination country E.g. UK
2) Go to a dealers or private seller and buy a bike
3) Provide an address when purchasing the bike for registration purposes
4) Ensure the bike has a 12 month MOT
5) Ensure the bike has 12 month Road fund licence (Must have insurance and MOT to do this)
6) Insure the bike (You will need an address and I guess an exchange of your US to an EU licence) This is a guess though so something for you to look up
Once all the above is sorted you will be free to travel europe as you please so long as you have the relevant VISA as required for a US national.
As for the freedom of movement around Africa. Carnet etc I can not comment. All I have provided is what you would need should you purchase a bike in the UK. I cant see this being any different for Spain, France, Germany etc.
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