Can the state impose any kind of restrictions on the exercise of the rights conferred by sub-clauses (d) and (e) of clause (1)? If so, under what conditions?
Yes, the state can impose any kind of restrictions on the exercise of the rights conferred by sub-clauses (d) and (e) of clause (1). The conditions under which such restrictions can be imposed are outlined in sub-clause (5):

(5) Nothing in 5[sub-clauses (d) and (e)] of the said clause shall affect the operation of any existing law in so far as it imposes, or prevent the State from making any law imposing, reasonable restrictions on the exercise of any of the rights conferred by the said sub-clauses either in the interests of the general public or for the protection of the interests of any Scheduled Tribe.