Hey Manu,
I would almost ALWAYS spike a sub into the ground or platform. It will let the sub driver do its job without wasting energy into vibrating the cabinet itself.
Carpet and a flat surface will both have their own sound. I would suggest you try both ways. With the carpet, the bass develops in a softer more diffuse energy by the time the bass waves hit your listening position. With a harder surface, you will have a cleaner more accurate response, but the sound integration might or might not be to your liking.
Either way, you will have to judge the sound yourself and see where your tastes lie.
Best thing would be to have yourself in the listening position and have a friend tweak the crossover frequency and gain. Go according to what sounds best to your ears and forget about the manual or speaker specs say.
Hope that helps out
Hoon chak de phatey!
PS:- Try this...spike the subwoofer into a wooden platform. Have the platform made such that there is an inch of extension from the edge of the subwoofer in each direction.
If the subwoofer footprint is 10 by 10 inches, the platform should be 12 by 12 inches.