Move Active Directory to the cloud - Office 365

My company currently have a local server which functions as file server, active directory, sql server+++ The AD domain is [login to view URL] and all users log in to their computers using their AD user/pass. All our employees have Office 365 subscriptions and users have email addresses which is username at company.com. The ideal scenario for me would be to transition to * active directory running on cloud server (azure) using Office 365 credentials (only one username/pass instead of two). * File server: If connected to company wifi then users will have access to local file server for speed. If not connected to company wifi then computer will use cloud file server. From user point of view it should be no difference beside speed. Should be the same network drive letters. * Group Policies and restricted file/folder access to file server should be same as today. * Printers should also work same as today.