Correct, do not move the VM to another datastore, just the host.
As far as your controller/disk/battery goes, I'd personally stick to migrating your VM's (if the system permits that,) and running the HP diagnostics. While I'm confident you need a disk replacement (btw are there any amber/red lights on this server's drives?,) I'm not 100% sold on the "battery replacement" warning. I've seen that over and over across different vendor's disk controllers for years. The HP diagnostics should tell you the real story behind what's going on with your hardware.