Remember that a light-year is a measure of distance, not time.
Not necessarily. By the time the light arrives here, its point of departure (and parts of its path through space) may have receded because of cosmological expansion, so its total travel distance, and its velocity, are no longer synchronized as they would be in Newtonian physics.
Your remark would have been true for the static universe that Einstein believed to exist when he proposed the first version of the cosmological constant (before 1929).