The white spiral on spinners was a tactical recognition marking or IFF, nothing more, nothing less. This is made perfectly clear in surviving orders and communications.
As early as February 1944 the orders for the spinner spiral were being issued but there was some confusion about which units should apply them and how. The definitive clarification was issued on 20th July 1944.
"With effect from today the recognition markings of our own aircraft in the Western Area will be changed as follows.
1(a) Fighters, including twin engine fighters, ground attack and reconnaissance aircraft are to have a black and white spiral painted on their spinners.
1(b) All other operational aircraft, no special recognition markings.
2(a) Captured aircraft, if flown operationally to be marked as 1(a) above."
The bold is mine.
Some units had adopted spiral on their spinners earlier, but not the standard width, one fifth that of the diameter of the spinner. Some units, not necessarily fighters, had been applying them in staffel colours from the beginning of the war. This is probably where the idea evolved from.
Night fighters started to operate in day light in defence of the Reich and this would explain why some applied the marking, though they were technically exempt.
The spiral was to 'rotate' in the same direction as the propeller.
2) answered above...walkway demarcations.
Cheers
Steve