Criticism is the path to knowledge!
Then, would Bran have a added advantage over Jon and Arya because of the Green Dreams? My guess is yes.
I would agree. Jojen's Green Dreams are proving to Bran that supernatural powers do in fact exist in the world and are not to be feared but embraced. Bran is also the only Stark to actively try to develop his power. He's also supposedly met his future teacher north of the Wall and likely will gain an even greater advantage to his development.
After going back, I thought you might be referring to the Three-Eyed Crow dreams. I think the Old Gods are taking special interest in Bran which is why he is being sent north of the wall through Jojen. I think Bran will be the only true "warg". The other children are just blindly tapping into this power, usually only at critical times.
Finally, how is it that the Stark children found these direwolves by pure luck of being at the right place at the right time and that they indeed match their personalities?
Coincidence or divine intervention? We've seen the power of Rh'llor through
Melisandre, Donadarion, Thoros, and UnCat. We've seen the power of the Other through the wights and undead. I don't think it's too outlandish to posit that the Old Gods sent the wolves as guardian angels for the Stark children. Why? I can only think that these Stark children would be be instrumental to the Old Gods' plans somehow. I think the presence of these wolves are like Jon said in the first chapter of AGOT, that these wolves were meant for the children of house Stark, whose sigil is the direwolf.
As to their personalities, when the children found them, they were just newborn pups. Growing up I would think that the wolves attempted to emulate thier beloved masters/parental figures. (remember Eddard, sternly ordered the children to raise them themselves, and to treat them with respect/warmth) Being unnatural creatures, and the development of that instinctual warging link between them, perhaps the children subconsiously asserted thier emotions through their wolves. Some of it stuck.
But, how is it that Arya continues to develop her warging abilities when she has been separated from Nymeria for quite some time?
I agree with Kiwi, while they WERE separated, I don't believe that such a deep bond which Arya and Nymeria shared, could be severed so easily. She was actually still in rather close proximity to her wolf. That is until she left westeros. I don't think she had any wolf dreams since after that. Futhermore, I think the random warging that the children experience are not so random. It occurs at critical times when involving the childrens' safety. (Jon and the Frostfangs) (Arya on the run from Bolton) Perhaps more subtle divine influence?
Also another note. Jon had no connection with his wolf after he went over the Wall with the Thenns. No wolf dreams, no sense at all. The wall has powerful spells sewed into it, according to legend and the words of Melisandre. There is indeed some magic that fuels this warging.
