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In the front viewport, turn on control points for this curve. Select the two endpoints, and then use 'scale1D' to scale the points in the x direction. Use the Z axis as the scale start point (use grid snap to snap to it!).

Select the middle point and move it down (ortho or shift!!). We now have a much more curved arc.

Turn off control points (hit esc a few times)

Use move to move the curve from its midpoint to the bottom curves endpoint.

Use sweep 1 rail to create a surface from these curves. The bottom curve is the rail, and the 2 arcs are the cross sections.

This is what we get, a double curved surface (this is much nicer than when we would have use a straight extrude for example).

This is how it looks in shaded mode.

In right view, create an arc like this:

Once again, move this arc from its midpoint to the midpoint of the circle (see image - click to enlarge).

From these two curves we will create a surface, also with sweep 1 rail. The closed curve is the rail, and the arc is the cross section. In the sweep options, make sure freeform is on and also 'do not simplify'. These are the default sweep1rail settings.

It should look like this.

Use trim or split to cut away the exessive surface parts. If trim or split doesn't work, you probably created surfaces that do not intersect properly. The main body looks a bit too thick, so undo the trim/split.

Select the bottom surface, and the curves that you used to create it. Move them all a bit higher.

Again trim or split. Now it looks better. Join the surfaces into 1 closed solid.

Use fillet edge to round the edges a bit (don't use a very big radius).

Select all the curves in the scene, and move them to another layer to keep things organized.

In the right view, make thin rectangle like in the image:

Use 'solid-extrude curve' to make it solid.

Now use boolean difference to cut away the rectangle from the main body.

Go to 'curve-curve from object-duplicate edge' to duplicate the edge on the top solid.

Select the duplicated edge, and use 'curve-offset curve' to ofset the curve a certain distance. You can enter a value or you can turn on the 'trough point' option.

This is what it should like (enlarge the image).

Select only the inner curve and use solid-extrude to make it solid. Use the both sides option so it extrudes in the top and bottom half of the main body.

Use solid-union to union the two halves and the middle solid together.

This is how it looks like:

In top view, draw a circle with its midpoint on the 0,0,0 point on the grid.

Project this curve onto the main body, and delete the bottom projected curve.