Some considerations:
1. What comes out of the
shower. No soap for sure, but you also have
urine (people
pee in the shower) and a small amount fecal matter. That means you may be feeding your fish (do you plan to eat the fish?) with pathogen-rich water. Not good.
2. The water coming off the fish tank is nutrient rich, but you have to have some way of aerating the fish tank. No oxygen in the water, fish die, you sad. Are you planning to take showers all day so you can oxygenate that water on a constant basis? If you see indoor fish tanks with large fish, they are oxygenating at an extreme rate compared to this design. This might work with minnows, but then you lower the quality of the water, as minnows don't do much nutrient cycling.
3. I don't think that fish would like your wood-ash and lard lye. The thing with fish tanks is the pH needs to be to their liking, which means constant measuring.
4. Not only the fish will be getting the pathogens, but the plants will be too. Unless you have a system in place to kill the pathogens.
If you have an excess of grey water, just put it into a tube and throw it on ornamentals in the spring/summer/fall; in the winter re-attach to sewer because you will be (assuming cool/cold temperate) inundating already wet ground with pathogenetic water.
Grey water can be successfully managed in reed systems with small fish who don't need a lot of oxygen. But this is not your case.
William