If you Pay'n'Spray in a way that would push you over midnight, you start the day over. Why? No idea, but that's how the game works.
The date is available 3 hours before the scheduled time. It showed up, as you can see on the minimap, at 21:00. I assume it would stay until 03:05 on Sunday, after exploiting the pay n spray bug which put you back ~21 hours. It's possible that it may have stayed available until the clock reached 03:05 on Monday, an additional ~27 hours, but I'm not sure. I doubt this would ever be useful, regardless if it'd stay an extra ~27 hours or not.
Our understanding of the game has evolved over the years and, with that, we've been slowly moving toward redefining the ruleset for the modern era of GTA IV speedrunning. All of these rules MUST be followed by those submitting top 10 runs, not just for world record runs, in all categories. I want to