Right, BT and DD both just give lifesteal and lifesteal-like effect respectively, with no special on-hit interaction.
gives 10% lifesteal, and as a separate effect does %health physical damage. Since it's physical damage, lifesteal applies to it.
similarly gives 12% lifesteal, and separately has effects that do physical damage. Since it's physical damage, lifesteal applies, although due to the particular passive on that item it only applies with 50% effectiveness.
Shiv's passive deals magic damage, and so lifesteal wouldn't apply to that as you said.
The phantom hit from sated does count as an extra shiv stack, and will proc the runan on-hit damage a second time as well.