Hey Burak,
I still dont have a solution to problem unfortunately. But i watched your video and checked the new FBX myself(i had to pass the file through Max first, delete the bones, reset xform, merge chais meshes and then link wheels to the chasis), and things go nuts the moment i plug the animation BP to the vehicle BP. There was another user(3ds Max time) having sort of last week and it was caused by crazy transforms. Your vehicle should work but i dont know why bones are acting weird with anim BP. Hope can see what we are missing.
Good luck!