They have a direct relationship, but it is not necessarily linear. There is no way to answer the what quality means without fully explaining video compression, which is very complex and depends on the codec. At a high level “quality” speaks for itself. Look up the meaning in a dictionary if you need to. Higher means better and bigger size; lower means less and smaller size.
Whether 100% quality means lossless depends on the codec. For non-hardware H.264 in Shotcut, it does mean lossless, but that is a rare thing. Most codecs are either lossless or not or require explicit lossless mode option.
What export settings would be the best with resp. to quality/file size relation?
This is impossible to answer because it is subjective and depends on the context and usage, but I tried to give you something that I think most people want in this ratio with the default options (aka Default preset) with H.264 quality 55%.
If i only want to adjust music/audio but the same video track unchanged how can i achieve a re-encoding without loosing video quality?
The only true way to avoid losing quality is to use one of the intermediate (visually lossless) or lossless presets. However, most people do not need true or nearly lossless. Start with the defaults, and adjust from there. It also depends on what you are doing with the files and their value.