I imagine that | z - 3i | is the same as | z + 2 | but looking at the changes to Re z and Im z.... | z - 3i | would be 3 units down on the polar plane (Argand diagram) and | z + 2 | would be 2 unit to the right on the Argand diagram.
I havn't had to graph things exactly like this yet (thanks to the delays of the HSC this year >_<)... I hope it helps.
For 1., you have to understand the form.
for |z - z1| = |z - z2|,
z describes the perpendicular bisector of the line joining the two points z = z1 and z = z2.
So on your Argand Diagram, plot A(3i) and B(-2) and find the midpoint of the line AB. Draw a dotted line that cuts through this midpoint, which is perpendicular to AB. This line is the locus for z for |z-3i| = |z+2|. Shade the region which satisfies the condition by subbing in a value on either side of the line.