Hi Raoul,
Maybe this explanation helps:
In "Solution 1" which I just described you are NOT using CUSTOM css CLASSES.
In "Solution 2" you are using custom css classes being: "c_popup4" and "c_txt_popup_panel1" (where c stands for custom).
In both my solutions you are using CSS which needs to be placed into a custom css file and needs to be linked into your bi app.
The difference in regards to css classes between solution 1 & 2 is that in solution 1 you only link your css file to your bi app (you are using the css selectors that are already available from sap), but in solution 2 you additionally need to assign your custom css classes to your text components for it to work.
That being said: I don't think you can use Solution 1 or Solution 2 without using a custom css FILE, but you can use Solution 1 without needing to use custom CSS CLASSES.
Custom css class = a css class that starts to exist in the html/dom of your bi app only after you assign it (define the name of it) to a component in the "Display > CSS Class" property of the component.
After you defined/assigned a custom css class to a component, the only way to define the css styles for this css class is by defining it in a css file.
Regards,
David