Sounds like the installer messed up the climate control wiring. May have bent a pin on the connector(s). I have a 2007 and also changed my head-unit. It was difficult to reattached the 2 climate control connectors( big hands and little space), but everything worked fine after I reattached them. I used a mirror to make sure they were connected. You should not be experiencing these problems after a head-unit install. If you had a shop do it - take it back and tell them it worked fine before the head-unit install.
2006 GT, Strut Tower Brace, Gas Hood Struts, FR Intake Plenum cover, Metal Fuse Box cover, Moroso brake reservoir cover, Rear shock tower brace, Front Bumper Lip Spoiler, JVC DVD Head unit w/ back-up camera, satellite Radio and USB input, 2 - 12" sub-woofers, 4 - 6"x8" speakers, 2 - 6.5" speakers to replace the door subs, 3 amplifiers, LED lights under the hood and in the trunk, chrome e-handle on parking brake handle, chrome cup holder trim, and trunk lid cover with running pony emblem.