When using Menu/Configure->Appearance and Fonts I found that I could try out different fonts and font sizes for a while, but when I increased them to 18pt, it stopped being adjustable. Now whatever the setting is, the font is always the same! (EDIT: It's the font for the element "All translation" which no longer changes, the others still do. I can start all over by deleting the configuration file /home/user/.config/qstardict, though.).
With "Popup window appearance" I was actually unsuccessful from the start - I wanted to increase the window of the displayed text, but changing "Default width" never had any effect.