(He it is Who has made you successors generations after generations in the earth,) meaning, all people succeed one another, generation after generation. This is like the Ayah:

(and makes you inheritors of the earth, generations after generations) (27:62).

(so whosoever disbelieves, on him will be his disbelief.) means, he and no one else will have to bear the consequences of that.

(And the disbelief of the disbelievers adds nothing but hatred of their Lord.) means, the longer they persist in their disbelief, the more Allah hates them, and the longer they persist in it, the more they and their families will lose on the Day of Resurrection. This is in contrast to the believers, for the longer they live and do good deeds, the higher their status in Paradise will be, the greater their reward, and the more beloved they will be to their Creator.