How does repeatetly moving food from freezer to fridge and back every day affect it?
I assume you have no food that needs to be kept frozen. If you do that's your greatest concern.
If, as suggested by your measurements, the fresh food never gets above the recommended maximum fridge temperature, the quality is going to suffer, possibly quite a lot, but the safety shouldn't, within the use by dates.
You may be able to keep the quality better by leaving the food in the fridge, but transferring a lot of ice from the freezer. I'd freeze several large plastic bottles, about 3/4 full of water, when the freezer is running, and move those into the fridge when you turn it off, leaving the food in there. Refreeze the next day. This is the approach used in many camping coolers, and it sounds like you have the ability to ensure the temperature doesn't get too high.
If it's so noisy that it's keeping you awake through earplugs, even if it's right next to your bed, that is quite likely to mean it's on its way to failing completely. The fact that your freezer is warming so fast is probably partly the unfrozen food going in and partly that it's empty of frozen stuff. It may also be a further sign of imminent failure.