1.) Strongest countries: Whoever is biggest and not Ming (though Ming can quickly join that crowd by rush-westernizing).
2.) Best idea groups: Pretty much everything military except Naval is good, as are most administrative groups. Diplomatic groups are kind of uninspiring, save Exploration if you like colonizing or Influence/Diplomatic if you like playing with vassals. Special mentions go to Humanist, Religious, Quantity, and Offensive.
2.a.) If you meant best National Ideas, basically everyone highlighted in "Rise of the Ottomans" plus Japan and Brandenburg.
3.) North America - Colonial Eastern America, followed closely by Colonial Mexico (both about 220 total base tax). The next best regions trail by about 70 base tax. This all assumes that you can bring the trade home, of course. Also, Ivory Coast is great to control completely because it directly feeds Sevilla, Bordeaux, and the English Channel, and assuming you are France, England/Great Britian, the Netherlands, Portugal, or Spain/Castile, you can use this to bring home all of that filthy lucre from Asia and impoverish your rivals.
4.) India's always been conquest, and now they're slightly harder to knock over. Not much harder, but you can't just ship five regiments and expect to stackwipe everything.
5.) They're all big, so yes. Ideas are nice and all, but in most cases, the biggest, richest countries are the most powerful, simply because they're big and rich. England would join them due to the obscene wealth of the English Channel node (every single non-end node eventually leads to the English Channel node), but the AI is still an idiot, so unless you're also on the British Isles, England is still pretty much a non-entity.
