Item synergy - does it exist?

+ , or - BC's physical damage reduces armor, but if using Tiamat or Hydra, does it affect all of the champions hit or just the main target?

or + , or - Athena's heal or Censer's attack speed, are they triggered by Crucible, Locket or Mountain?

There may be others, but only these i can think of right now. Do passives trigger from item to item or just from ability to item? And for Athena's heal, does it affect only one target, the main one or everyone affected by shields, like Karma's aoe?