IS0/IEC 27018:2014 establishes commonly accepted control objectives, controls and guidelines for implementing measures to protect Personally Identifiable Information(PII) in accordance with the privacy principles in IS0/IEC 29100 for the public cloud computing environment.

This is false, as this is the definition of Portability and not interoperability

This is True
Like security and compliance, BC/DR is a shared responsibility. There are aspects that the cloud provider has to manage, but the cloud customer is also ultimately responsible for how they use and manage the cloud service. This is especially true when planning for outages of the cloud provider (or parts of the cloud provider's service).
Ref Reference: CSA Security GuidelinesV.4(reproduced here for the educational purpose)

The data controller(typically the entity that has the primary relationship with an individual) is prohibited from collecting and processing personal data unless certain criteria are met. For example, if the data subject has consented to the collection and proposed uses of his or her data, then the controller may collect and process data, according to the consent agreement.
Ref: Security Guidance v4.0 Copyright2017, Cloud Security Alliance