“Can you fly a Permit plane to all of Europe except Belgium and Spain, with no prior arrangement at all?”
It depends how you define “Europe”. You need permission for the Channel Islands (again just a paper excursive), but I think they are not technically in Europe.
“or training?”
Training is possible now provided you own the aircraft. It is increasingly common to buy a “Plastic Fantastic” and train in it as you are burning 15lph of Mogas and many enthusiast instructors charge little more than expenses.
IFR is now a real possibility, but the devil will be in the detail, which we will not know for some time.
I would be very surprised if a Stampe can get an LAA permit, but I do not know for certain. Give LAA engineering a call if you need to know.
Rod1