Is it possible to use CommVault to the VCenter 6.5 Linux?
What other methods can be used with VCenter 6.5 Linux?
Do you mean the vCenter Server Appliance?
Migrate VCenter 6.0 (Windows) to VCenter 6.5 Appliance (Linux).
Backups will not break down?
Should be fine, just make sure you are on v11 SP7 for 6.5 support. 6.5 is not available on 10 and there currently no plans to support it.