The wall is stunning and creative, but sadly, I have to agree with the consensus expressed on all your threads: this wood should have been bone dry, carefully checked over piece by piece for holes, insects, existing fungus etc., and probably treated and certainly well sealed before before being installed. At this point, I would cut my losses and take it down. Once the pieces are all down, it's possible that if you thoroughly scrub off all fungus with a bleach solution, then let them dry bone dry (preferably in a wood kiln or perhaps a DIY drying shed), then treat and coat, these pieces could be reinstalled. Even that depends on the conditions they'll see - if this wall is exposed to lots of steam or grease you'll be having new issues before long. Also, is the wall itself dry and solid? Any chance water is leaking or oozing from somewhere and adding to the issue? What species of wood is this? Some species are naturally more fungus resistant and appropriate for this than others. Long story short, I'd recommend finding a different way to cover the wall - with ceramic, galvanized metal, or with a really scrub-resistant paint.

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.

there is many types of support to be used for counter top for long lasting work... as ... 1) brick wall which takes 2" , 4" or 6" thickness space which is not good for below space as we will waste space for storage under counter... this is used where heavy material is used on top of counter for cutting any food items... 2) marble support... which will take 35mm thk space double support... 3) furniture base if the kitchen working person is using the sink properly for washing purpose and the gaps between the sink and counter top has to be sealed properly for leakage free to avoid any damages for below storage, as i will not prefer this in other area... this can be used only in foreign countries...

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.