5.34(a) To distinguish between Consumer 1 and 2, let u2(y1,y2)=y2^2exp(y1). Note that xi+yi=6 for i=1,2. To find the contract curve, maximize u1(x1,x2) subject to u2(6-x1,6-x2)=U. The answer is x2=2. (This assumes an interior solution but it is easy to show the endpoints also belong to the contract curve.)
5.34(b) Fair allocations must be Pareto efficient and hence on the contract curve (x2=2). To be envy free we must have u1(x1,x2)>=u1(6-x1,6-x2) and u2(6-x1,6-x2)>=u2(x1,x2). After a bit of work, I got that this implied 3+0.5ln2<=x1<=3+ln2.
5.34(c) Unlike the core, I do not know of a theorem which says the set of fair allocations shrinks as the economy is replicated. It is easy to show that each consumer of a particular type must get the same allocation in a fair allocation.