For the rectangles, have you thought about creating a pattern out of straight boards and placing it underneath the item you're cutting? You then use the plunge router and plunge a small hole in the middle of the part you're cutting out. Then switch to a pattern cutting bit and just guide the router along the pattern on the bottom.
For the semi-circle, just cut out a full circle on a pattern board, then cut the circle in half and put a straight edge along one side and repeat again with the pattern cutting bit.