Well, you have a lathe....

And lathes can be used to do milling. You can remove the tool post and clamp a small vise (Like a drill press vise) to the compound slide. Put an appropriate end mill in the lathe chuck. Lay out and put your part in the vise and away you go.

This is the short answer of one way to do it. You could also grind and file if you don't think the above is within the limits of your equipment and/or ability.

As far as attaching the rod to the piston, you could either thread both parts and Loctite them together or assemble parts, cross-drill them and use a pin.