Firepower management server and Firesight system are 2 names of same thing.
starting from version 6.0 the central management server software to manager firepower appliances is called "Firepower management center".
Prior to that it was called Firesight management center.
Yes Firepower 8130 appliance can be managed by Cisco Firepower management center (virtual or hardware)
The management Firepower 6.0 version doesn't support HA as of now (its probably coming in next version).
The firepower 8130 can be configured in HA. Please take a look at the guide here. It should be able to shed more light on this.
http://www.cisco.com/c/en/us/td/docs/security/firepower/60/configuration/guide/fpmc-config-guide-v60/Device_Management_Basics.html#ID-2242-0000085f