No, they're not. Inside the European union (which I'm sure is what you meant), while you have the right to move around and work as you wish, most people don't do it and don't want to. In practice there's language barries and cultural barries all over the place.
True for most, but it's not the demographics of Rovio employees (or at least the main employees). Would be good to have a more exact statistic.
Absolutely not. You can start by looking at one article in wikipedia where it is immediately apparent that countries are running their own systems, with substantial differences in rules and rates. The Nordic countries (such as Finland) are generally in the lead.
Sure, unemployment benefits are different in their structure, but the end result is similar. Finland may be better but the systems in other countries are not really behind.
Rovio is in this case a prime example of a company which has benefited substantially from Finland's school system for skilled employees (they're one of the absolutely best in the world), Finland's stable democracy and their stable economy.
I'd say citation needed. Do you think education in Finland is so much ahead of that in France? England? Sure, for basic school Finland is one of the first ranked usually, but this does not correlate with market success!
Also, Google, Nokia, Intel, etc take a lot of talent from less 'educated' countries like India, Brazil, or slightly less than Finland like USA, Ireland, where nonetheless you can find very talented people.
When they're asked to pay back, they flee -- an extremely immoral act which I sincerely hope will bite them in the ass.
Well I wouldn't blame them, since being successful results in huge taxes.
The reasoning of making bigger companies pay more taxes is not something I disagree with, until one realizes companies are mobile nowadays.