Any height provided you met the emergency egress requirement.

In North American jurisdictions you need an emergency exit from bedrooms. If there is no exterior door, then you use a window. If you a window it can’t be more than 44″ from the floor.

There are many reasons why, but I’m going to assume you are asking about highrises for living and offices.

One of the better reasons is to allow more people on the same amount of ground.

Second, for economics.

Let’s say a given area currently has 1 family per acre. These are nice fairly open areas. But, if all the areas fill up with 1 family per acre, but more people want to come it stars to make since to place more families per acre.

Once you get to about 16 families per acre you need to change how you are placing people. The simple answer is to go up (usually going up is about 10 times easier than going down).

Again once go 5 levels up things change again.

Right now most conventional construction can take you up to about 60 levels above ground or about 15 levels below ground. Beyond that you start needing to get creative.

So, back to the question, the reason we build highrises is to allow more people to get together than would be possible standing on the ground.

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.