Fay, I've lived in South Georgia and in a 1904 farmhouse in rural middle Georgia, so I've had some experience. All but the most ramshackle houses would have screens. In the country, as others have said, the water source is almost all wells and that requires electricity. If the pump shuts off for almost any reason, it will have to be reprimed. (Envision me at midnight in my gown and slippers taking a container of water outside to the well house, while cursing a blue streak.) Alabama does have artesian wells, which will supply water without a pump.
The people across the street from us had no plumbing, so they still had an outhouse. You occasionally run across people who've kept their outhouses up, but they're now pretty tightly regulated. However, if you can get water from anywhere, you can flush a toilet by pouring water into it. You'd have a septic tank work for some years.
In terms of critters inside the house, we had palmetto bugs (giant flying roaches about 2 inches long), ants, field mice, packrats (that was fun) and squirrels in the attic. Outside there'd be lots of mosquitoes, plus paper wasps and way too many caterpillar like things eating the garden and shrubbery. There are fireflies in early summer. There are the aforementioned fire ants. They build big mounds and their bite is like being touched with a soldering iron, then the worst itching ever. If it's a brushy or overgrown yard, there will be probably be chiggers and ticks. Deer are a big problem in most rural areas, and they busily munched on my garden too.