(2)Look as the charge is conserved on the conductor( it is not connected or earthed), so as soon as the attractive force from the rod is removed, the electrons reorient themselves again so that the body becomes fully neutral
(3) If we bring an uncharged body near a charged one, they will attract each other, but won't repel in any situation...so repulsion can occur only if both bodies are charged.eg uncharged paper bits are attracted by charged comb
(4) Earthing is actually the process of making potential of body = zero
btw, answer should be (d) and not (b), plz check
because to make potential of conductor = zero, negative electrons must flow from earth into conductor