I don't know if the size of the tank makes a difference in cycling time. If you are going to seed the tank with filter media from another tank you can either put it in the filter in the new tank or yes, you can just place it in the tank. The beneficial bacteria that is in the seeded filter media will then start growing in your new tank. Be sure to "feed" the tank with a source of
ammonia (pure ammonia, flake food, raw shrimp, etc) so that the bacteria doesn't die off before you add your fish. I would do daily water tests and within a few days you should see that you are cycled.