Now that you're there, go here
http://www.oldbritts.com/ob_tech.html and down to 'Commando Clutch Plate Info' to see what you have. I'd be leery of the Barnett plates unless you have the cush drive, or a 71 or newer rear wheel. If you have the 69/70 clutch, I'd stick with what you have unless you really want to change. I have 14K miles on my original 69 plates and they are still in tolerance and work great. Plus the Barnett plates take different plain plates too, the thicknesses are different for the early and late years. That's in the Old Britts article.
Read about the different clutches and make a decision. I bet you can make your current parts work fine. You need to get that friction plate off the solid plate, maybe soak it in something, I hate to say brake fluid, but I've never had any problems getting oil/grease/whatever off the friction plates, they seem to work with oil or not, at least mine. I just clean them with carb cleaner or mineral spirits or petrol. Heck, some people even sand them on concrete.
Welcome to the Commando learning curve, there is an end to it and every time you go down the road, you'll be thinking about all these little details.
What keeps it from opening? Not sure, I wonder if your diaphragm is broken over the wrong way, that's been known to happen, I didn't look at it that closely. The springs should be pointing towards the inside or clutch side, not the outside and when you pull the clutch lever the rod should be pushing the stud towards the outside to release the clutch plates. The springs on the diaphragm hold the clutch plates together tight with no pressure on the rod.
Dave
69S