sleep cycles and evolution

Factual Questions
1

This thread about forest moons caused me to think about sleep cycles on other planets.
http://boards.straightdope.com/sdmb/showthread.php?threadid=76914

An earth day has approx. 16 hours of light and 8 hours of darkness. Humans are awake approx. 16 hours and sleep for 8 hours. On fictional planet X a day lasts 48 hours, with 32 light hours and 16 dark hours. Do the native animals on planet X stay awake and alert for 32 hours and sleep 16? Is there some biochemical reason why animals need to sleep according to earth hours? If we transplanted earth animals to planet X would they switch their sleep cycles? How far could this lead, what if the day was 100 hours of light and 33 hours of dark?

2

Doesn’t an earth day have, on average, 12 hours of light and 12 hours of dark?

I mean if I, in the USA, have 16 hours of light and 8 hours of dark wouldn’t that mean that those in Australia (the opposite side of the globe from me) have 8 hours of light and 16 hours of dark?

Am I missing a mathematical equation somewhere?