I'm not too clear on the various kinds of air-dry clay you've listed. DAS seems to make several types of air-dry clay? (one of which is terracotta earth clay and another a paper-type clay?). I guess the other two are different brands of regular air-dry clay but more expensive so may behave better, crack or shrink less, take finer detail, stick to itself better, etc?
You can read about some of the differences between the types of clay in my answers here:
http://answers.yahoo.com/question/index?qid=20100621051506AA53JtDhttp://answers.yahoo.com/question/index?qid=20110507004411AAmELzg (read the "list of facts" there especially)
As for using an air-dry clay
with a polymer clay though, you can certainly do that in various ways. Just remember that air-dry clays shrink, need sealing, can't do as many effects, can be coated with any kind of paint, take longer to harden and must "dry" to harden, may crack or crumble, etc, etc.
Air-dry clays can be heated in the oven, but that's usually done just to speed up their drying. And since they're made from either paper/wood, ground minerals-stone, soil, or flour, they can take a fair amount of heat, or a huge amount of heat, depending on which is used...there's nothing in any of them that could melt though.
So you could:
....make and bake your polymer clay pieces, then glue them** to the dried/hardened and perhaps painted air-dry clay; for some info about that, check out this page:
http://glassattic.com/polymer/onlay.htm >
Non-Clay Onlays at least, but some of the polymer clay onlay techniques would be helpful too if you need to curve or shape the undersides of the polymer clay, etc.
....use hardened air-dry clay as an armature under the raw polymer clay if you want it as a large sheet for "covering" or just for raw pieces of polymer clay, then use some kind of adhesive (or a mechanical hold) between the clays, and bake the hardened air-dry clay and the raw polymer clay together
Check out these pages at my site on "covering" air-dry clays and other paper or terracotta surfaces with polymer clay and ways to do that, and on using various kinds of armatures under polymer clay including paper-based ones:
http://glassattic.com/polymer/covering.htm >
PapierMache,Cardbd,Paper...or
Terracottahttp://glassattic.com/polymer/armatures-perm.htm >
Paper-Based Products http://glassattic.com/polymer/beads.htm >
Covering a Core >>Clay Cores
Air-dry clays are porous and polymer clays don't stick well to porous materials, so you'll have to use some kind of adhesive between them.
If both parts are hardened, most thick permanent glues should work (some will be flexible, some won't, if that matters).**
If the polymer clay part is raw, you'll need to use a glue that can be heated, so you could use a permanent white glue (the stronger the better), or probably liquid polymer clay (but that's thin and not tacky).
...Or pop off the hardened polymer clay and glue it back on with almost any glue.
...Or you could create a
mechanical hold of the polymer clay on the air-dry clay instead of the adhesive hold (or in addition to it)... e.g., wrapping the clay around something or having it go in/down/around some other dimensional surface or item on or in the air-dry clay. Or you could wire the pieces together, etc.
Also, if you leave the raw oil-based polymer clay in contact with water-based/porous air-dry clay, some of the oil in the polymer clay will leach into the air-dry clay over time and leave an oily spot. You can create a barrier under the polymer clay though by coating the hardened air-dry clay with clear polyurethane or another permanent water-based finish, or with acrylic or latex paint, or with thinned-down permanent white glue (PVA) or decoupage medium, and let dry.
Btw, polymer clay also comes in larger bulk amounts. Many of the brands/lines can be purchased in 3/4 lb to 1 lb sizes (online, or some in art supply or craft stores, etc), though some will be more brittle after baking in any thin areas or any projecting ones (like plain Sculpey, also called Polyform in art supply stores) and will be mooshier to work with. If you're interested in checking out prices and availability online, look on this page too:
http://glassattic.com/polymer/supplysources.htm >
Mail Order** glues, etc:
http://glassattic.com/polymer/glues-Diluent.htmHTH