I'm starting to get parts together to build a MT using a rectangular cooler and copper manifold. Should I buy soldering the copper pieces together or will it be better to just put them together and not permanently solder them?
Both. Solder together some connections, but not all of them. This will give you more structure, but still allow you to take apart and clean. If you can end up with 4-5 pieces when it is taken apart, it will make your life much easier.