First of all, none of what you asked can easily be generalized across all of Europe. But let me try to be as general as possible.
1) It depends very much on the program, in the good programs in Europe there is not much difference. Lower ranked programs usually let students research 'something' without steering them towards asking better questions.
2) Even if you want to stay in Europe it may matter, but only for very few select schools. And of course it depends on which institution you do your PhD at.
3) Not universally true, but good Europeanprograms look at your potential reflected by academic achievement, content of letters and your written statement.
4) Again depends where you come from. I would say mostly yes.
5) Strongly depends. In Tilburg (where I'm a faculty member), we have very students per adviser and I at least try to meet with students frequently and advance their projects. Other good places in Europe will do the same. Not so good places might use PhD students to just do work for the advisers.
6) If somewhat successful so far help, otherwise hinder.
7) Funding at EU programs is often more generous than in the US as you often get a 'researcher salary'.
8) I strongly suggest you also look at Bonn, Munich, Amsterdam and Tilburg. Happy to chat about the benefits of Tilburg.