1) Normally, a captain and co-pilot would take turns. However, there are situations in which it would always be the captain flying the plane. Certain aerodromes, for example, are captains-only aerodromes. On the other hand, some captains let the co-pilot fly the first leg when they haven't flown for a while, like after their holidays. No nautical tradition, though.
2) Sounds very much like the ground power cable. Your are right about the refuelling ports being under the wings. Another hose often seen is the one for the air conditioning which is mostly plugged-in under the fuselage.
3) ATC will clear you for a STAR or SID. If you are cleared for one you are obliged to follow the published route. Very often, however, ATC will give you radar vectors, i.e. they tell you to fly a certain heading. But generally it's always ATC who tell you what to do.