Noob question about dishwasher tailpiece install

[tjstogy]

So, the black pipe in the back is open at the top with the dishwasher drain hose stuffed in it- this has caused a huge leak recently when it fell out. I was looking online and stumbled across a "fix" for the previous persons improper plumbing job http://amzn.to/1TWTuJ2

So- a couple questions...

1. To properly install this it should be directly under the sink drain above the p-trap (currently the white pipe) correct?

2. Why is that black pipe even there (the one in the back)? Can I just cap it off at the lower joint and if so with what?

3. I'd like to affix the drain hose and fill hoses to the back of the cabinet to make room in the cabinet- is this advised and if so what is the necessary clamp called?

Thanks!

 

[phishfood]

#1 Yes, that is the correct way of attaching the dishwasher drain, so that there is a water seal trap between the sewer/septic and the dishes in the dishwasher.
#2 Not the best way, but you at least need to add an air admittance valve to the riser pipe in the back, so that the trap will have some kind of a vent.
#3 Any kind of 2 hole plastic pipe clamp that will fit around the piping will work. Make sure that the dishwasher drain hose gets strapped up to the bottom of the countertop, so that in case of a drainage clog, nasty water can't make it's way back into your dishwasher.