The wood has to reach what's called Equilibrium Moisture Content (EMC), which is different for various areas of the country/world. I don't know about end grain slabs, which is what you have, but the rule of thumb for lumber air drying (vs. kiln drying) is 1 year for each inch of thickness. Moisture leaves the end grain faster than the side and/or edge of the boards, so in your case the drying time will probably be shorter. If it is not dried in a controlled environment your slabs are going to split radially, due to drying too fast.

I am not exactly sure whether the material is similar to Corian or quartz manufactured in India and used for kitchen platforms, but I won't advice you to use it considering our use of turmeric in cooking. Better someone else be gineapig before you spend your good money on untested material.

Installing a 19 mm thickstone carcass (ie, the back, sides and floor slab) is an almost foolproof way to prevent termites. But this requires experienced and skilled labour to make sure that the plumb line is maintained. This seems to be a specialty in places like Jaipur and Gurgaon, so that's where you get this kind of labour. However, for fixing the shutters and drawers, you will still need carpenters and I must warn you that drilling into stone is again a laborious and slow process. And coordinating between the stone layers and carpenters can be a bit of a pain. I have worked with this option and also with plywood alone. Ceramic tiles on the wall are no protection against termites

I have used both with good results. The main difference between Quartz and Granite are 1) price, 2) colour range. Granite generally works out cheaper, because you can buy the exact quantity you require. Quartz comes in large slabs of specific sizes- standard size being roughly 10'-0" x 4'6", so there tends to be more wastage if you don't plan the cutting well. But Quartz is pretty and comes in a wide range of colours and can be re-buffed at a later date. Quartz also comes in various thicknesses- the most commonly used being .75" to about 1.25". And especially when you use dark wood cabinets in a kitchen or bathroom, beige and white counter tops work very well. Some people go even with coloured counter tops like blue, orange, yellow. Natural stone in light colours tend to be porous and stain easily, so I prefer to go with pure black which is safe.