I would think England would be the most vegan-friendly place within the EU. Most of the other EU countries have pretty heavy dairy industry and not a lot of compassion for (specifically farming) animals, unfortunately. The southern EU-members like Spain and Italy are not so pushy on the dairy but have no clue about veg*nism (generalizing here). Cities would be better than countryside.
I have no idea about the citizenship or taxes issues, I even think gambling may be illegal in a couple of countries, you need to look that up maybe on one of the EU websites. They have Q&A sections.
Switzerland, while being one of my favourite countries in Europe, is not an EU-member and is very, very hard to get into. They further toughened their immigration laws a few weeks ago.