Well, if you ask me butterflies are really bad pets. They don't live very long, if you want to keep them as long as possible their natural habitat is quite difficult to reproduce and they require a lot of care, depending on the species. To keep them in a big space like yours is especially difficult because they will fly towards the light and as you already observed will mostly fly against the window. The only thing that I would do is locating all the important things to that window (the cabbage plants), so they will find it there. If you want them to reproduce it would probably be a good idea to check if you even have both sexes.
To the first question, they probably died because they didn't feed enough. I don't know what's in the "nectar mix" you're feeding them, it sounds certainly weird. Just giving them plain sugar water or honey water will do. But you have to feed them by hand. They won't find a food source reliably in captivity. You could try to offer them flowers, but that's usually not enough. You can't provide as many flowers as a butterfly would need. Yeah, I kinda answered the rest of the questions already...
Greetings Dennis
Hey Dennis, thank you for your input. When you say butterflies are bad pets, do you mean butterflies specifically or also moths? Would moths be easier to take care of because they are active in the dark (and thus do not fly towards the windows as much)?
Based on your feedback, I have decided to at most keep the butterflies until they have laid eggs, and release them afterwards. I did have both sexes, and one female laid eggs in the small box that I kept the caterpillars in. One butterfly had a damaged wing and lived out its full lifetime when I fed it by hand. It does indeed seem easier to keep them in a smaller space. Do butterfly cages (e.g. http://www.silkmoths.eu/cages.html ) help in keeping the butterflies from flying against the mesh, towards the light?
I believe the nectar mix is just honey water with a few minerals. I wanted to compare it against the honeymix I used earlier.
Kind regards,
Karin