Bicycle Mechanics - Newbie and Dura-Ace Barcons

Howdy. I'm trying to install 9sp DA barend shifters on my drop bars. I am very confused. I've got the shifters in the bars, and the downtube stops installed just fine. Included in the package are two sets of housing and one thing that looks like a washer, but it has a ring around the inner circle, like a rivet, or a top hat with the top cut out. What is this???

Also, the two lengths of housing are different lengths. One is about 11 inches, the other slightly more than double. I don't understand why they are different lengths, or how exactly I am supposed to route the cabling. Is one side used traditionally without housing? Or are these cables specifically to be used at the derailleur end, meaning that I should cut housing for the shifter-downtube cable stop part.

Finally, what is the 4mm ferrule for?

Thanks!

The "top hat" is an insert that goes in the plastic under bottom bracket cable guide to reenforce the hole the fixing bolt goes in.

The short housing piece is used between the rear derailleur and the housing stop on the driveside chainstay. The 4mm ferrules are used at the end of this piece of housing and at the ends of the shift housing where they enter the dt cable stops.

thanks for your help!