Here is some help. On #1.

Suppose that A=sup(S) and B=sup(S) is A is not B then one is less than the other: say that B<A. The by definition of supremum, there is an element, x, in S such that B<x<=A. Do you see the contradiction?

On #3(a). We know that between any two real numbers there is a rational number. Then there is a rational number between x & y, r_1. There is a rational number between x & r-1, r_2. How do we know that r_1 & r_2 are distinct? For each positive integer n>=3, there is a rational number r_n between x & r_{n-1}. How does this prove the statement?