1. Can this be used with a licensed VMware Virtual Center Server??
Yes it can.
2. When will an update for 4.0 Update 1 be released??
HP is usually a little behind the generic release. There are issues with the HP modules and update 1. Stay at 4 until there is a release from HP
3. Can this work on HP Proliant DL380's with HP hard drives installed?? (It should, double-checking).
Yes.
4. For monitoring, does one install SMH into the host's vMA server??
The HP version of ESXi includes CIM modules (similar to SNMP agents) that will provide monitoring information to vCenter.