Unfortunately customers cannot schedule their own backups to meet internal BC policies currently.
However if you look at the roadmap for CRM this feature is coming allowing you to run backups to Azure.
Customer backup and restore
UPDATED
As part of our trusted cloud investments, Dynamics 365 (online) customers will be able to do their own Dynamics 365 backups and restores to meet their business data recovery plans. Customers will be able to back up their Dynamics 365 database to Azure storage using a secure data transfer (not the public Internet). Customers will also be able to download and connect their backup to an on-premises environment. This feature provides several potential scenarios, including a local developer experience.
Availability
Application
Dynamics 365 for Sales
Dynamics 365 for Customer Service
Dynamics 365 for Field Service
Dynamics 365 for Project Service Automation
As for point 2). A service request to MSFT should allow you to migrate from one tenancy to another, but that will only work for another online environment and not on premise.
Hope this clears your query.