There are several ways to answer this question.

In general: vertical. Literally, 8″-9″ depending on use and jurisdiction.

For most publicly use spaces most designers will use a 7″ riser (vertical) and 11″ tread (horizontal) or 6″R and 12″T as the general layout with adjustments for the final heights and materials used.

For lower steps a portion is used based on a typical human stride of roughly 23″-24″.

Private stairs can go down to 9″R and 6″T, but this is typically uncomfortable to most people and would require use of handrails.

Stairs that have a rise higher than 9″ is called a ship ladder and require handrails along its length for additional support.

Vertical to near vertical systems would usually be called a ladder. Steps or rungs tend to be between 9″-12″ apart.

Generally, they would be called facades.

Keep in mind that there are many alternative names that relate to specific parts of the facades, or that they may be termed similarly to movie and theater sets.

But, from a general architecture point of view, they would be facades.

In a hot-arid region, like a desert; yes.

In other regions you lose efficiency as the humidity increases and temperature decreases. Around the point where the outside temperature reaches the cooling water temperature it starts acting as a water heater. So, it is highly dependent on your environment.

The simple answer is no one owns or possesses the center of the Earth.

The UN has operational guidelines on these matters of non-recognized territories. Typically, coastal waters are defined as 20 miles out from mean tideline. Territory air rights extend to low orbit, although some nations reject any stationary or near stationary objects above them. Underground is less obvious.

Right now humans (mines for all real purposes) can only extend about a mile down. Small shafts can extend down about three miles. Given the diameter of the Earth (just under 4,000 miles) this isn’t very far underground.

There are two working examples that would likely be used should the matter come up. Antarctica and the International Space Station. In Antarctica, a nation comes along and sets up a base. That base plus an operations area around the base (typically 20–100 miles depending on the declared research and agreements from adjacent bases). There are many exceptions to these that were developed by agreements, so imagine broad guidelines here.

In the case of the International Space Station each module operates like an embassy of the sponsoring nation. All space around it is international, and crimes or disputes depend on who and where it occured.

So, back to the question. In order for a nation to claim the center of the Earth as territory, a human-operated base would need to be set up within a short distance of it. Likely, in order for the UN to accept this claim that nation would need to allow members of UN nations to the base periodically to conduct their own research.

Like most materials found on Earth very little of it is already in a usable state.

Basically, there is a lot of water, but as we get more and more people the “ready to use” water is quickly spoken for.

There are still huge amounts of water left. Only now it requires prep-work before its “ready-to-use”.

But, since its been so easy to get “ready-to-use” water for so long we don’t have many places that can cleanup whatever has been mixed into the water (dirt, pollution, salt … whatever).

So, the simple answer is straight forward simple contamination coupled with higher demand.

For the most part, yes.

There are many examples of sand-like materials you wouldn’t want anywhere near fire, but you’re unlikely to readily get ahold of these.

The simple answer is an eave when continuing the slope of a roof and a rake when crossing the slope.

Beyond that, there are many many specific and regional names.

For design, purposes most rain “hitting” is considered vertical. In high wind areas, a 45-degree projection can be used much like shadow projections.

More typically, we are concerned about water shedding and ponding.

Water shedding is where the roof, or other elements, direct the water, often concentrating the flow to specific areas. Normally, we want to direct water away from door openings, and window openings to a lesser extent. Gutters and diverters will help with this but can become overwhelmed during heavy rain.

Ponding is a buildup of water in an unwanted area. This happens a lot on flat roofs or dead-end valleys of roofs. Plugged up drains or insufficient drainage tends to be the cause. This increases the weight on the roof very quickly and can cause leaks by overwhelming or undermining the waterproofing system.

So, again the sort answer: vertically.

The problem is that this is a loose question.

The actual answer is almost anything. But usually plywood or OSB sheathing with a waterproof membrane between the sheathing and roofing.

Much beyond that, you’d need to specify the type of metal roof and what you’re roofing as these can change things dramatically.

The main reasons the Earth’s core is so hot is:

1. Pressure – literally all the dirt and rock squeezed together. Thought to represent greater than 70% of heat production.
2. Friction – different density and temperature layers grinding past each other. Thought to be 20%-25% of heat production.
3. Radioactive decay – nuclear decomposition. Thought to be less than 2% of heat production.
4. Chemical reaction and other processes. Basically everything else.

As other answerers have mentioned we are looking at the Earth 4.5 billion years later. So, yes the Earth is cooling, but at a progressively slower rate.

On the cooling:

1. The Earth can really only lose heat by radiant methods.
2. The Earth has an insulating layer, the crust, many miles thick, but only represents less than 0.1% of the thickness of the Earth. As the Earth continues to cool the crust thickens providing more insulation.
3. The Earth’s atmosphere and oceans redistribute the heat that makes its way to the surface across the whole fairly evenly.
4. Eventually, it will cool down to solid rock as you think of it today, but this is billions of years into the future.

Just as a parting thought, the vast majority of the heat we feel on the surface of the Earth comes from the sun, not the Earth. This isn’t a comment on intensity so much as the level of insulation between each source.