Yes the bisector of angle C is correct for (b) and the perpendicular bisector of BC is correct for (c).
This is how you draw them (see picture).
Point of compasses on C and any radius smaller than BC or CD but greater than half their length, draw an arc to cut BC and CD. The blue arc is all you need for the angle bisector but I've shown the whole circle, because we can use it for part (c). Also, using the same radius draw a circle with centre B.
Now we need to draw the green arcs. Put the point of the compasses on the point on CD where the blue arc cuts. Use a radius a bit larger than before and make one of the green arcs (or you could draw the whole circle). Do the same on BC where the blue arc cuts so that the two arcs cross. Now you can draw the red angle bisector. That's part (b).
The blue arc was part of the circle centre C. You already drew the circle centre B, so now you can draw the red perpendicular bisector where the two circles intersect. That's part (c).
Because the question is about a park, we can expect that we only need the red lines that are inside the park area.
Note that the position of A makes no difference to (b) and (c) because we are only interested in the side BC and the angle C, none of which involve A. However, to draw to scale in (a) you probably have to assume that angles D and A are right angles.