a/c and remote starter?
#1
#3
#4
I don't think that it will damage the A/C system but it does put more of a load on an expensive starter. I'd bet that it will lead to the starter wearing out sooner than if the A/C was off during starting. Turning the A/C off before shutdown will also reduce the air temperature that is coming through the radiator because the condenser will not be putting heat into the airflow into the engine compartment. This will help to cool your turbo more quickly. Just to be fair I don't realistically think that this would be a very significant amount but it might make a small difference. Just my 2 cents.