If all of the water in the Caspian Sea were poured over the summit of Mount Everest, would it freeze, and how much higher would it make the mountain?

That amount of water would probably heat up the mountain and wash away a fair portion of it. If the water was slowly put on the mountain cold enough to be snow or ice it would continue to roll/slide down the mountain to melt at lower elevations. The height would not increase by much. Maybe …

What are the new promising non-sand based building materials being researched today?

There is a huge amount of research going into laminates and composites of various materials (structural). Foamed homogenous materials (structural). Sapphire as a structural material. Various grown crystalline structures that behave like metals. Glass as a structural material. Memory metals that behave differently under various conditions like heat or electricity. Strand bundled sections that change …

Which new material that is corrosion resistant can replace iron and be used in construction or development of other structures?

You have a number of choices. The simplest would be iron with a corrosion resistant coating such as paint. and by corrosion resistant I’m assuming you mean oxidation resistant. Otherwise you have stainless steel or aluminum. Depending on your requirements you also have plastics and resins, but typically these get expensive and may not have …

Why can only 2/3rd’s of a plastic be recycled?

As I understand things you have generally two categories of plastics. Thermosets and thermoplastics. Thermoplastics lend themselves to be recycled, thermosets may or may not lend themselves to recycling. And of course, as each has its sets of material properties many things must be constructed of non-recyclable plastics in order to work properly.