Right, here we go.
Here is a photo of a plunger clutch layed out. There should be one thick steel plate and four thin steels and five friction. The pressure plate is the correct one and goes against the last friction.
The thick steel is the first one to go in the basket, then a friction and a thin steel and so on. The pressure plate on the plunger models is also the last steel plate, it goes against a friction plate, not a steel.
Your basket is the correct one,these are the only ones to have a twin row chain, but at some stage in its life someone has machined off the flange that has the studs to hold the cover on. This should not be a problem, it will work ok as a wet clutch.
One thing to watch is the quality of the friction plates, sometimes the cheaper ones are thicker than the originals and can cause problems, I only use Surflex plates.
With the early plunger models without a seal the engine oil can get into the primary as you have found. This is not a problem but if your bike has sat for some time and has wet sumped then you need to check the level in the primary as well. Also only use a motorcycle specific oil that is suitable for wet clutches as a lot of car type oils have friction modifiers in them and they can cause problems with the clutch. Normally this would not be a problem but you will have a wet clutch.
Good luck.