You forgot that y>=0: the rope must be above ground level. Let the center of the circle be at height h. Then, y=h+a sin omega t. You have to determine h, a, omega. Your guess about omega=2pi is correct (since the rope turns one time per second.) Since -1<= sin omega t<=1 and 0<=y<=7, you get h and a.
For problem d, determine for which values of t you get y=5.25 (using calculators or tables for the sine function.)