Most of them do look younger than Thorin except like Balin and his brother.The 13 dwarves are the ne who have accepted to join Thorin.
The purpose of this endeavour is to take back the gold from Smaug. Dwarves are rather greedy, but they are not foolish enough to think they could take back the city all by themselves.
The Arkenstone is still in the Mountain.
As for the timeline :
About 200 years before The Hobbit, King Thror (who is not named Oakenshield, that's Thorin's surname), escapes Erebor with his son Thrain II and his grand-son Thorin II Oakenshield. About 10 years later, he gives his ring (the last of the Seven) to his son and leaves for Moria. He is killed there. Later on, Thrain II, because of his ring, gets greedy and wants to return to Erebor. He is captured by Sauron's minions and taken to Dol Guldur. Sauron takes his ring. Gandalf enters Dol Guldur. Thrain gives him the key and the map to Erebor. The rest is related in The Hobbit.
So Thorin is more than 200 years old. In the movie, he looks like a middle aged dwarf, but in the book he is the oldest of the 13 dwarves(well, maybe after Balin). He has a long white beard.