is it possible a head gasket could be installed wrong so it would make a car heat up when the thermostat is in but run cold when the thermo is out it runs cold? or could the head just be f***? i want to start driving my mustang soon since i swapped in a ka but my buddy who i bought the engine from never got it to run right with the thermo and just ran without it and ik it was bled a lot even the small screw bleeder on the head what loosened to let air out and the whole engien was rebuilt last spring so idk what to try or anything i need some guidance on what to do

You can never install a HG wrong, they go in one way. Its just ka's have a bad habit of trapping air in them. But you also better make sure the thermo was put in correctly, with the little pin being up top. Then jack up the front end of the car 6-8in off the ground. Turn the car on and turn on the heat all way up, add coolant as needed and you should be good to go!

It's going in a mustang and I'm using a Nissan wiring harness for the body so I don't have a heater I was just gonna put a 180 degree bend hose on the heater core pipes so I was just gonna lift it high and if there's still air leave the rad cap off and go for a drive

Moving to KA, but as long as the deck and head are straight, clean, and everything was properly prepped and torqued I would say you need check the thermostat and make sure its installed bleed hole facing up... I always drill t-stats myself, then follow the how to bleed proceedures.

Jack the front of the car up front tires off the ground 4-6 inches.
Take off radiator cap
Take a 2 liter pepsi bottle cut it in half and use some black electrical tape and wrap the bottle neck a little, or get a cooling funnel
Flip it around and place the bottle neck were the radiator cap was at. Pinch off over flow line if not using the funnel.
Now start filling it with coolant about half way
Remove bleeder screw
Close bleed screw after you get a nice even stream of coolant
Squeeze the upper, and lower lined and burp out the air
Add antifreeze until you over fill the rad by a quart
Turn the heat on full blast
Start the engine and let the engine run after 3-10 minutes the thermostat will open and suck in the excess antifreeze (ambient temp affects time)
Fill it again but with about a half of quart.
Let it run until no more bubbles come out. Squeeze hosed time to time.
Replace cap, unclamp overflow hose and then shut off the engine, fill over flow 1/2 to 3/4

Coolant funnel (best to have)