turning on aircon after start will add burden to your engine once the clutch engaged. personally i think this is good to speed up the engine warm up process.

whether is required to turn off the ac or not when u turn off the engine.. this can be an optional. Modern car will delay ac from starting when u first crank ur car. If that mechanism is working fine then all good. For me i will still turn it off to conserve battery during cranking as with ac on the blower will run when u r in acc mode. Personal habit thou.