im not sure where you got "c>0" from in your first answer. I hope that does not mean "marginal cost > 0" because you are told that the marginal cost is zero.
One method for part b would be to:
start by finding the profit if the company DOES price discriminate (find the profit maximising price in both markets).
Then find the total demand function (D = x1 + x2 = .....) and find the most profit that can be made if a single price is set for the whole market.
Then identify the conditions needed for the profit to be higher in the second case.
However, i would have thought that was the same method you would have used in part a?