If two careers share some characteristics or skills, can you buy advancements that counts to both careers? not really at the same time I suppose but would it count when the player switched back to his starting career if he had, lets say raised agility in his other career.

No, it used to work like that but not now. Agility+ for one career isn't weighted against Agility+ in a second career. That being said having certain familiar traits will make switching to a new career a little cheaper. But it doesn't work the same way it did in past editions.