Barrel composting of vegetable leftovers provides me several buckets of composted material each spring. I believe the ~20 liter buckets I have on my balcony don't get hot enough to kill pathogens ... but haven't had problems yet. I imagine a 120L barrel seeing some sun could reach suitable temperatures ... but then you can't have worms ...
This could be collar rot. Overhead watering too much water are factors. It's fungal.
According to the link you can try to build up soil around the lesion early in the process. Alternatively, you could try to cut some way above the lesion and replant the top of the plant. You'll find lot of materials online on how to grow from cuttings.
If it's fungal don't ...
This is a classic example of damping off. https://en.m.wikipedia.org/wiki/Damping_off
This process probably began when your seedling was very young.
In general, young seedlings need very little water. You want to keep the soil moist but not saturated. When in doubt, don't water.
If you want to avoid both synthetic fertilizers and animal waste (as discussed in some of the comments), there are some organic fertilizers that are based on waste products that would have to be disposed of otherwise.
The Bokashi method for example turns kitchen waste into liquid fertilizer on a household scale.
Some commercial producers also claim that ...
There are a lot of organic fertilizers both solid and liquid you can use and they are more than enough to produce great crops.
The amount and type of fertilizer depends on the plant though so you are going to have to do some research on your own.
The main nutrients are NPK - Nitrogen, Phosphorus and Potassium - and you can run into trouble with lack of some ...
Yes that is possible, you can use organic fertilizer instead. For example cow or chicken manure can be used. I have these in dried granules form, I just add a hand full every month or so when I think the plants need some extra nutrients. But there are more organic fertilizers, check here on wiki if you want.
It's hard to say with certainty without knowing how strong your indirect light is. So, I'm just going to share the most likely candidates that come to mind, whether or not they'll actually work for you.
I've found that Jerusalem artichokes don't need a terrible lot of light to get big tubers in my garden. I could see them doing fine with even less. Note that ...
Nettles likes shade and is quite tasty and healthy ... but most consider it a pest so let's skip over.
Radishes grow like weeds - quickly and even in the dark.
And lastly, again rather as a comment, Pelargonium - the toughest flower on the planet. I once forgot one in the dark without water for 12 months. When I found it it had nearly died. Point being, this ...
It is almost impossible to grow vegetables in house shade. If the area gets two to three hours of fairly sunny partial shade, you might be able to grow black raspberries or gooseberries, but I don't know if your grandma would like you to grow perennial vegetables there.
Depends what you mean by "shade". If you mean dense shade of a maple forest ,not much will grow. If you mean no direct sun but open sky , then leaf crops like spinach and chard should be good. May try coles ( cabbage, etc ) , not great but you may get something.