Three or more layers are needed. Paper must be kept moist to keep from blowing away. Any type of mulch is excellent. Yes, but should be composted first or at least one year old. Yes, excellent source of organic matter.
More gardeners prefer to use shredded leaves.
Yes, any kind of mulch or organic matter will open up clay soils. Never add sand or sandy loam. If the cotton had been sprayed with a defoliant which contains arsenic the hulls should not be used as a soil amendment. Most cotton in this area has been treated with a defoliant. For mulch but not for compost.