The pipes that come off of the bypass valve will be horizontal toward the wall. http://www.discountwatersofteners.co...ssemblies.html shows pieces that include the choices you select from. The self-install kit they sell uses John Guest http://www.johnguest.com/Home/about-...echnology.aspx connectors to mate with your existing plumbing. I don't know if you can attach to what is existing there after taking a saw to it; I doubt it. The flex aspect sure looks useful to me. You can use conventional plumbing and you screw in with 3/4 or 1 inch pipe fittings -- depending on which size bypass valve that you choose.
If you just start unsoldering the copper, I am concerned that you will damage your plastic pipe. Others will know how to deal with this. Maybe they will recognize your plastic and tell you how to connect a new fitting to that plastic.