How long does it take for the moon to cross the sky from moon-rise to moon-set?

About 12 hours but depends how far you are from the equator and the time of the year. At the poles the moon does not set in mid-summer and does not rise at all mid-winter!

The duration from moonrise to moonset is cyclic on the lunar cycle, and is surprisingly variable over this short period. For example in March 2010 for Phoenix AZ it varies from a bit more than 9.5 to almost 15.25 hours. This is because the moon's orbit around the earth is at a 5° tilt relative to the earth's orbit around the sun

For exact times deduct the moonset time from the moonrise time given at one of these: