What is the best home treatment for very sore achy heals which have a very thick tough skin? also what's the best lotion for dry sandpaper-like feet?

The thick or dead: Skin should be removed. This is best done by a podiatrist. If you don't have insurance consider a pedegg available at a drugstore. I like the high concentration urea creams to help moisturize a foot.

Soak: Soak your feet every night before bedtime in lukewarm water for 10 minutes or so. Then apply a urea &/or salicylic acid based cream. Wash it off every morning. If you use salicylic acid, select the weakest strength -1% maybe. Gently rubbing with a pumice stone will help as well.

Keratolytic creams: For non diabetics. Soak feet in aveno oatmeal bath for 20 to 30 minutes and apply a keratolytic cream such as 20% urea (carmol 20) or 6% salicylic acid. Stronger creams are available from your dermatologist.