(a) Plotting good 1 horizontally and good 2 vertically, consumer 1's indifference curves are vertical straight lines and consumer 2's indifference curves are horizontal straight lines. Consumer 1 prefers more good 1 so they want to move to the right. Consumer 2 wants more of good 2 so they want to move downwards.
(b) Any allocation in the core must be Pareto efficient (page 186) and we can improve both consumers by moving downwards and to the right. The furthest we can go downwards to the right is when consumer 1 gets all of good 1 and consumer 2 gets all of good 2.
(c) Consumer 1's demand function is x1 = (50/p1,0) and that for consumer 2 is x2 =(0,50/p2) so the excess demand function is z = (50/p1 - 100, 50/p2 - 100). The Walrasian equilibrium is p1 = p2 = 1/2 to clear the market. (Prices have been normalised to p1 + p2 = 1. The demand functions then follow from the budget constraints.)