Hi,
regarding gypsum and lime, they are both calcium carbonate or calcium magnesium carbonate based products - so limestone, dolomite, seashell, bone, even eggshell. Gypsum, also known as plaster of Paris, is calcium carbonate in powder, so pulverized dolomite lets say, form, and was developed as a faster drying and simplified version of lime for stucco work and has really no mechanical or binding uses. When the calcium carbonate is processed in ovens to around 900 - 1200 degrees C, (The process goes further but I cannot really explain in English), carbonic acid is cooked out of it and it is converted into calcium monoxide. Water is added which converts it into calcium hydroxide. Calcium hydroxide is the white, or slightly off white when it comes from seashells, powder that you would buy at the shop as lime. Once it is used, the process begins to reverse itself as it takes up carbonic acid from the environment and reverts again to calcium carbonate. So after 100 years it will be harder than it was at 1 year or 50 years.
It is not only self-restoring, it is self regulating in that it takes up and releases water from the air, it is somewhat elastic as you would see if you ever walk through the streets in Amsterdam and it is a disinfectant - good for painting the stall and chicken coop - among other very fine qualities. The big disadvantage is that once it is processed it begins to revert and so cannot be kept indefinitely.

If you do use lime in your clay mixture that is fine but be aware that you cannot then reuse it, whereas without lime in there the clay can be re-used.

On your other point, I've got clay tiles on my barn, and have used them in other situations and depending on specifics they can be an ideal roofing material.