Defensive player. Primary job is to mark the opposition winger. Good fullbacks are able to get forward when in possession and add an extra attacking dimension, by linking up with the winger or putting in crosses.

Some players are more adaptable than others. All teams need a good structure across the park, there's no point on only having attacking players for example, because you're going to get fucked. Certainly there are more attacking and more defending structures, and it is not uncommon to see an attacker subbed off for a defender when defending a lead, or vice versa.

Possession is much more fluid in soccer than in American Football. Yes, it's to get the ball up away from the danger area. It's also common for goalkeepers to play short passes to retain possession from the goal kick.

I'd imagine that all professional clubs in Europe (and much of the rest of the world) have some sort of youth set-up