This is from another post that I read so I can not vouch for the accuracy of it. I hope it helps with part of your question.
You will need to create a 3-d model :
Draw your ellipse and the major and minor axes in a plane.
Use one of these axis lines to trim away half the ellipse.
Then switch to a coordinate system centred on one end of the half-ellipse and with the end of the ellipse line perpendicular to the xy plane.
Draw your groove shape and a small part of the internal solid cross-section as a closed polyline.
Use the extrude command on the polyline and specify the nearest end of the ellipse as a Path for extrusion.
(Extruded polylines cannot self-intersect, therefore your polyline cannot extend to the centre of the ellipse).
Mirror to get the other half.
Draw an irregular polyline in the plane of the ellipse to cover the central hole, extrude it upwards, and union it with the earlier solid to close the central hole.