I'd like to set backups for my Azure VMs and manually restore from them (hence, create new VM from it), in case if something goes wrong. My VMs also have SQL Server 2016 (Windows) and MySQL Server (Linux) running. Azure Docs are pretty confusing for such use case. This article, for example, describes how to backup Azure VM https://azure.microsoft.com/en-us/documentation/articles/backup-azure-arm-vms/ it doesn't mention consistency and if will SQL Server 2016 and MySQL databases be damaged in case of an emergency restore. Another documents mention replication, but only for Hyper-V, VMWare, On-premises Server. Which one is Azure VM? So, my questions are: What should I use for my use case? What type of VMs are in Azure?
At the time of backup the Azure Backup extension sends a command to the VM to flush all writes, then it takes a snapshot, this should mean that your backups are consistent. This is similar to the way VM backups are done in Hyper-V and VMWare and should allow you to restore VM's just fine. However, the only way to confirm all this is to test, restore your VM's to another location and make sure it works, you should be doing restore tests anyway.
As far as replication goes, if you are using IaaS VM's (rather than SQL Azure) then if you want replication you would need to set this up yourself using the functionality of the software (i.e. always on replication in SQL).