How can I make kimchi with everyday ingredients?
To answer your specific scenario, kimchi has myriad variations using any number of vegetables, from perilla leaves to Korean radishes to napa cabbage. There are forms of kimchi that involve no chilies (white kimchi), some involve a lot of water and bear little resemblance to the typical napa cabbage one (mul kimchi). The main constraints for Korean-ness of kimchi will be that you've fermented it (for all of the types that I can think of, anyway), and that it doesn't stray too far from familiar Korean flavor profiles (rules that you can break if you've got a deep enough foundation in Korean culinary traditions).

Napa cabbage isn't particularly hard to find in Europe, however, so I'm not sure why it would need to be substituted. For whatever reason, it was called "Chinese cabbage" in Germany; I'd be surprised if you couldn't find it. If I wanted to make the typical cabbage kimchi, the hardest thing would have been finding the right kind of chili powder, which I was able to obtain without too much trouble when I was a 20 year old student there many years ago. Then, the typical small bits of raw oysters or other kinds of fish or dried shrimp can reasonably be substituted with locally available ingredients (and some regions in Korea don't always use those ingredients anyway).