Mostly right.
The Path of War (ObSec) and Craftworld Attributes apply to a Craftworlds detachment where all units share the same Craftworld. You can add other detachments to the army without affecting that.
Stratagems require a Craftworlds detachment that isn't an Auxiliary Support Detachment. Again, if you have one Craftworld detachment and other detachments you can use Craftworlds stratagems. They can apply to any unit with the relevant keywords, which could be from a non-Craftworlds detachment.
Warlord traits need a Craftworlds warlord - not necessarily in a Craftworlds detachment. Likewise Relics can be assigned with a Craftworlds warlord.