How long to cycle??

Water won't make any difference, other than to import wastes. Splitting the media would be better, or at least squeezing out some sludge from the media onto the new media in the 10. Done properly, it can allow you to immediately stock the tank, though the more cautious route is to seed the tank, and then fishlessly cycle it.

I agree with Oriongirl. Either filter media or some of the top layer of gravel or decorations will all import good bacteria. The actual time of a cycle will depend on the amount of bacteria you bring over and the amount of waste you are feedign them. If you are planning on adding fish right away then I woudl suggest adding a few at a time, testing the water every couple of days for ammonia and nitrite and do water changes if those register. If after the first week things are fine add a few more fish and continue that way until you are fully stocked.