When viewing the full set, the male avatar has a spectrum-styled 'hawk hairstyle; I am wanting to know if this item exists and/or what it is called.

there are no hair pieces in that trunk except for a beard .

http://www.subetalodge.org/costume_trunks

the hair on the male HA in the pic of the Symbol of the Galactic Empire

Definitely not part of the trunk, it's a basic Subeta hairstyle from the Wardrobe with custom coloration (can be done with the Hair Salon today.).

ok, thanks