Hi Marcel,
Here is Email form in my Customer Service Hub:

It seems that you had added some customization to the default Email form? I didn't see Subject, Addtional and System Data sections in Email form of my environment.
From your latest screenshot(the first), it looks like some text are hidden due to width of Description section,
could you check whether more text was hidden due to width limitation with inspector?

If you could find more text, then increase the width out description section or set Email form layout to one column.
Apart from this, "ActivityEditorControl" would be the reason that images can display directly inline, but the control is only available in Enhanced Email form,
so we couldn't add it to other forms.
Regards,
Clofly