Hi Vivian,
1. We do have our own AD and use DirSync to sync our user, which does all work.
2. We don't use Exchange only Office 365 for our email.
3. We want to migrate our Office 365 from out current Domain to a new Domain for example current domain = Inframon.com to new domain = inf.com.
4. In the new Infrastructure we are going to be having a DC in Azure and a DC on premise with them replicating.
Hope this helps. I will PM you the case number now.
Many Thanks
James