After filling up the turrets I start storing a couple of stacks of ammo in the ships inventory. Dumping that into the distribution system during flight makes things a little easier.

Not an expert but these systems are fairly self-contained and robust. A few things that can be checked easily is that the fan spins, the radiator is free of debris and some compressors might have a sight glass for the oil level.

Any other checks regarding performance of the system, leaks and refrigerant level require you to perform a full refrigerant discharge and recharge. That takes special equipment and some time so no one in their right mind would do that for free, unless they can then force/guide you into some kind of upsell situation.

Larger systems might have some kind of oil filter/catch-can that you might be able to check easily but I’m not too sure on that.

After all heat pumps are just plain old A/C units with a reversible cycle.