At the time of writing, there are 8,819 featured quizzes in the English section. JetPunk displays 5 quizzes a day between January and September, and 6 a day between October and December. This means that any one quiz has either a 5 in 8,819 or 6 in 8,819 chance of making the FP each day, depending on the season.
From these figures, we can derive (with some knowledge of the Binomial distribution) the chances of any specific featured quiz making the FP over different time periods. They are as follows:
Weekly: 1 in 252 (Jan - Sep) / 1 in 210 (Oct - Dec)
Monthly (30 days): 1 in 59 (Jan - Sep) / 1 in 49 (Oct - Dec)
Yearly (365 days): 19.5%, taking seasonal variation into account (or about 1 in 5 chance)
Note that these calculations assume that daily FP quizzes are chosen completely at random, which may not always actually be the case. But it should give you a rough idea of what to expect with your featured quizzes making the FP.
(By the way, does anyone know who or what gets to decide which quizzes to put on the FP each day?)
I don't really know how the frontpage works but my best guess would be moderators have some kind of way to edit the page for future dates
It's likely a bit of both.
I don't know how common it is for "old" featured quizzes to return to the FP. I see it happen all the time with the highest-ranked users, so it's probably just a draw-people-in-for-the-takes kinda deal.
Same thing with spotlights, new spotlighted quizzes enter a queue waiting to be put on the User Spotlight.
Also, on January 19th (MLK Jr day in the US) this year there was an extra quiz on the FP. Do they always do this on important holidays outside of the October to December season? Just curious.
(MeMeMe told me the other day he thinks QM was trying something new, but I'm not sure if that's really the case or not although they didn't seem to do this last year)