are you sure you have heatstrips or another form of back up heat? the wiring is hard to confirm without knowing where the other ends go.

 

If you have heat coming out, but not as warm at some registers, it's not the thermostat.
Call the guy who already got paid for the job.

 

i definitely have an all electric model with the heat pump / condenser AC outside and the emergency unit inside. (at least that is what the home inspector told me)

 

unfortunately most inspectors don't know much about houses let alone hvac details. have you measured the temp difference at registers?

 

Also the black wire is not connected to anything, and there is a brown while coiled up behind other wires also not connected. I have some novice wiring experience and as far as i know black is usually hot, so what could that be?

 

I guess it is possible that i do not have the "emergency" heat coil. The sticker on the unit looks to say "no heat kit"

 

More than likely, the installer didn't mark the panel with which heat kit he installed.

Take a picture of the high voltage wiring going into the furnace. Don't take any doors off.

 

high voltage into unit

 

Looks big enough to me for you to have a heat kit in it. You probably do.

 

Also at the main unit, the brown and black wires are not spliced to anything which would explain the brown and black disconnected at the thermostat unit

 

Sounds like your all setup.

Sounds like you have more of a duct issue.

 

You have a 8 wire bundle wire and need only 6 wires the other 2 wires are spares. As far as the E ( emergency ) Auxiliary jumper with the white wire looks correct to me. They even used the correct colors going to terminals . Goodman for the most part uses blue colored wires for the C . The white wire goes to your electric heat relay . During normal operation the heat pump is first stage heat through Y , 2nd stage heat is through the AUX./E , during emergency heat mode you power your electric heat through the E/AUX. If you feel cooler air from some vents than others may be due to those vents are furthest from the air handler , loosing temperature before they come out of the vents.

 

Its possible, it the way your duct work is attached to your air handler that is causing the air temp difference.