The turbo would not do anything to get those codes. They are specific to the heater control for the sensors but please check this on Gendan and Ross's sites.
I think you have 2 separate issues and looking for a common solution.
Have you checked the air filter is not blocked and checked the turbo wheels for excessive play, any smoke from the exhaust, unusual smell from the exhaust (fish is usually someone having fun), blocked exhaust (failed Cat)? Again a smoke tester can check for such a block.
Yes i think maybe 2 seperate problems but maybe one problem being caused by the other. It has an open induction kit thing on it, cheap filter which ill sort out when its running right, ill try another filter though see if it makes a difference.
No smoke or smells no...but was going to remove the turbo and check it over this weekend for any play or wastegate issues