Start with cleaning the walls, windows and high shelves, moldings, etc. Use an extension pole with a damp mircrofibre if you're not into ladders. I found a large microfibre mop works great for dusting the walls. Don't forget the dust clings to wood moldings, windows, top of doors and their frames, light fixtures and the bulbs too!! Literally, you have to wipe down every surface, whether it be in front of you, above you, hiding from you or beneath you. LOL Vacum the floor really well after you're finished with all the other surfaces then mop with a mild solution of vinegar and water. Of course if you have carpets, just vacum really well. I just started cleaning our new new house and boy, it is not an easy taste. Well, it's easy in that the dust comes right up, but there is so much to clean!! Good luck.

Clay certainly will crack up if it is subjected to a lot of heat. When I fitted a fireplace, I was told to use concrete rather than plaster around a tight fitting mutli-fuel stove. I ignored this advice and the plaster cracked! I imagine clay does much the same. Here is a link that might be useful: The costs of reinstating a fireplace

I don't know if you're interested in buying a piece of equipment, but I have a Hoover Floor Mate that I use to clean my hardwood floors (and I have a lot of them). We have natural wood floors from wood that was cut from our property. Since it has been laid, it continually shrinks and expands, so I always have a crack somewhere (deeper than bevels). I'm always amazed at all the stuff the Floor Mate gets up. It has 3 cycles. The first is like a vacuum, the second scrubs (rotating brushes that won't damage your finish) with water or a solution or your choice, and the final is a suction where it dries the floor so you don't have any wetness (or very little) left behind. I got the attachments (good for cleaning grout, tile, etc), but don't use them very often. I highly recommend this machine! I've cleaned up a lot of sheet rock dust in my time and it seems to glue itself to everything. I'm sorry you're having to go through all this. But I'm sure the end result will be beautiful! Here is a link that might be useful: Hoover Floor Mate Reviews

If you decide to vaccum it, and I don't know of any other way to do it, you can use a shop vac. but you really should get a high density, disposable paper bag to put in the vac. It really does make a difference. Otherwise the finest dust just comes back into the room. After you've vacced and if things still seem dusty you might have to go over the walls, ceiling and floors with a damp rag. I do the walls and ceiling wiht a rag tied around either a broom or a dustmop.