That tool is for installing Campagnolo square taper BBs. Keep hold of it though, it's the same tool for Campagnolo cassette lockrings. Hand tight is probably good enough for Powertorque cups I think, as they slather them with threadlock but otherwise an external BB cup tool is what you need. Shimano HT2 and Campagnolo both use the same pattern but be gentle, those Campagnolo cups mark very easily.
Wavy washer coil thing is a bearing preload spring to compensate for differences in BB shell width. Black thing is a seal that goes over it. They are referred to as "spring and gasket" on p6 of your pdf. So it goes:
- Cups
- DS crank
- Spring clip on DS cup
- Spring and gasket onto NDS
- NDS crank
- Crank bolt