I'll use t for theta

consider r = 4sin(t)

r^2 = 4rsin(t)

x^2 + y^2 = 4y

x^2 + y^2 - 4y = 0

x^2 + (y-2)^2 = 4

which is the eqn of a circle centered at (0,2) with r = 2

As to your second question as t varies from 0 to pi/2 r varies from 0 to 4

completing half the circle . as t varies from pi/2 to pi r varies from 4 back to 0 completing the circle.