Learn English – When do we use “wait for” and when we use “wait to”

Wait a minute

This is pretty generic and informal and is often used idiomatically to ask someone to pause what they're doing until told to continue. It doesn't usually mean exactly a minute, any more than "wait a second" means exactly a second.

Wait for a minute

This sounds like something that you'd find in directions/instructions:

Wait for a minute and then add the oil to the pan.

In this case, it more often means exactly a minute, though it's not required. The exact timing here is more important. You would be unlikely to find native speakers who would use this in the idiomatic manner of the previous example.

Now, does this carry over to numbers of minutes greater than one? Sort of?

Wait five minutes

Will usually mean five actual minutes... otherwise, why bother specifying the number. As mentioned before, "wait a minute" doesn't really mean a minute... one could end up waiting for a few seconds or several minutes in the end. Even in directions, you'll often find they've left out the "for" in this case:

"Remove from stove after one minute of boiling and wait five minutes before topping with granola."

So what about with the "for"?

Wait for five minutes

This isn't wrong. Using it this way is not ungrammatical at all, it's your choice. It's not required and you will definitely find examples of it, particularly in more professionally-written instructions:

Slide the whole skillet under the broiler, and wait for five minutes, until the crumbs are golden brown and the salmon is done.

This is also discussed, though not to a great degree, in Cambridge Dictionaries Online:

Wait means ‘stay in the same place or not do something until something else happens’. We can use it with or without for:

• Put a tea bag into the cup, then add water and wait (for) a minute or two before taking it out.
• I phoned the head office but I had to wait (for) five minutes before I spoke to anyone.

Although all of your examples illustrate exactly the same question, for clarity's sake we'll take your examples in order:

• 3 kilograms OF oranges or 3 kilograms oranges?

3 kilograms of oranges.

In natural speech, "of" would be included. You might see it omitted in a shopping list, but never in everyday speech or writing.

• 80% OF humidity or 80% humidity?

80% humidity

"Of" is omitted in common usage. The "of" is included, though, when we reverse the order of the terms. You might hear a meteorologist predict either: "Tomorrow, we will see humidity of 80%" or "Tomorrow we will see 80% humidity."

• At the spacing OF 3 meters or at the spacing 3 meters?

At the spacing of 3 meters

Here, normal usage will include "of." A list of instructions—for instance, to a carpenter—might read:

"Height 3 meters, Width 2 meters, Spacing 3 meters."

• 100 kg OF N or 100 kg N?

100 kg of N

See "oranges" above. In narrative use, we would include "of:" "Be sure to bring 100 kilos of N!" A list of constituents, though, might read:

200 kg Ammonium Perchloride
100 kg Nitrate of Gallodinium
150 kg Phosphorus

• 30 inches OF precipitation or 30 inches precipitation?

30 inches of precipitation

The "of" will almost always be included.

• 50 meters OF height or 50 meters high?

Either of these usages may be grammatically correct, depending upon context. "High" is an adjective, and "height" is a noun, though, so this example differs from the previous ones. In normal usage, though, you would almost never see "It has 50 meters of height." Instead, one would say either:

It is 50 meters high.

Or:

It has a height of 50 meters.

It's important to understand that you will frequently see technical or scientific writing, technical support documents, instructional manuals, and lists of things, which omit "of" for brevity's sake. There is no "rule" governing such usage except that "of" should only be omitted when its omission makes a statement unclear.