Yes, the red line, or ring, was supposedly the punishment, and was applied before the introduction of the washable distemper ID paint, with the Geschwader supposedly then being known as the 'Red Ring Geschwader'.
White was used as the ID colour by JG53 (and some other JGs) at first, and later changed, as with other units, to yellow, as it was more visible in certain lighting conditions.
The common belief is that, soon after Gunther von Maltzahn took over as Kommodore, in November, the 'Pik As' badge reappeared, but there are photographs in existence, purportedly taken in August 1940, showing the badge in place on the engine cowling. One of these also shows a particular pilot who was lost in September 1940, which would suggest the photo could not have been taken after this time. There are. of course, photos and written records, showing that the red ring was also in place on other aircraft of the Geschwader at this time.
However, it's possible that the source of these photos, a former aircrew member of JG53, might have confused the date of the photograph, although unlikely, considering the in-depth detail recorded by this pilot.
The over-painted swastikas were on aircraft of III Gruppe (although I think I have also seen similar on Geschwader Stab A/C, but these might have been Stab, III/JG53 - would need to check). Apparently, this was done under the orders of Hauptmann Wilcke, the Gruppenkommandeur at that time, as is generally thought to be as a political gesture.