As far as I know, they share an ICD since they are similar effects. I could be wrong and haven't tested it, but based on the damage proc ones sharing an ICD I'd make the same assumption here.
No the icd is independent
The only time they share same icd is if you have two exactly identical relics.
Even the conq version of a relic will stack with its partisan counterpart however for tanks doing sous ineffective as outlined in my first post