I think what you are describing are threaded inserts. Grab ahold of the threaded part you can see protruding from the socket and turn it out (either by hand or it may be necessary to use channel locks... be careful not to damage the threads.) You will then be able to thread in the winter plugs. Don't remove the screws or the faceplate.
When you removed the filter while the pump was running, it may have sucked some air and now has an airlock. Try breaking open some unions to release air and looking for an air release valve around the pump plumbing. Beachcombers often have them at the top of the plumbing assembly and are usually marked as "air bleed" or something similar.
I would not adjust the pressure switch until you have done this.
After some research, I learn the filter cycles may not be changeable on your model. From your description, it seems that you have the basic model, and if so, then you are not able to change the filter cycles. I suspect that you have a bad pump control relay. here is a Lite Leader tech manual, may be of some help. http://www.hottubworks.com/SpaParts/PDFs/B...lLiteLeader.pdf
I am suspect that the transformer is the problem. Because it shows only 80v, I suspect the problem is within the circuit board. I am not familiar with your system, so I cannot say for sure, but the board will probably need to be replaced.
To be clear, it sounds like you are still powered up, but not at full power? Good advice to check the voltage, especially when the pumps shut down. If the red or the black show low or no voltage, then you know the problem is with the supply. If you are at 110 on each, then you know the problem is within the tub.
No worries, the water will not freeze until it gets much, much colder than that. I have 1 customer who has been ordered by the fire dept to keep his pool circulating all winter because he has no fire hydrants near by, and his pool is on constant standby for fire protection all year round. He has no issue with freezing.
Besides, worst case scenario, just turn on the heater! (lol)
The manufacturer may be identified on a rating plate attached on the inside of the equipment compartment, or on the base under the skirt outside the tub.
I am not an electrician, but it seems to me that if you are going to get a ground fault or overdraw it is just as likely if the breaker is in the house as outside. My guess is if the wiring and breaker are sized correctly, and the wiring is done properly, you will have neither of these problems.
OR 07 is not a code I have ever seen before. As suggested, reset the circuit breaker. What other problems are you having? I wonder if they could be related.