Remember:
Less head-scratching, fewer mistakes
I could not find anything simpler than this. Straight from the OxfordDictionaries.com
Use 'fewer' if you’re referring to people or things in the plural (e.g. houses, newspapers, dogs, students, children). For example:
People these days are buying fewer newspapers.
Fewer students are opting to study science-related subjects.
Fewer than thirty children each year develop the disease.
Use 'less' when you’re referring to something that can’t be counted or doesn’t have a plural (e.g. money, air, time, music, rain). For example:
It’s a better job but they pay you less money.
People want to spend less time in traffic jams.
Ironically, when I’m on tour, I listen to less music.
'Less' is also used with numbers when they are on their own and with expressions of measurement or time, e.g.:
His weight fell from 18 stone to less than 12.
Their marriage lasted less than two years.
Heath Square is less than four miles away from Dublin city centre.
So, the sentences in concern:
There were no less than 50 people in the dining hall
In 25 words or less, please summarize what took place
Fewer calories (but 'less calories' has also ingrained in the language these days. Maybe, it's used where the number of calories is not specified. But still, don't consider this as a rule)
The hamburgers should contain no/not less than 50% meat.
Less than 5% of the population will be affected.
Further reading recommended here.
Worth noting that 'no fewer than' is an idiom which means the number you are describing is surprisingly large. Beware of using it that way!
I can see you've done a lot of research, and have come up with an ambiguous understanding which is a shame (English sucks). I hope I can help clear the air for you. :)
Your first instinct about there being no article needed in the first example was correct:
Without air and water, living things could not survive.
In fact, in most of the examples your sister found to support the being the correct particle, the could actually be removed entirely:
Birds and insects could not fly without air to support them. Without air, humans would not be able to fly either.
We can’t survive for more than a few minutes without air, so why isn’t air as much a part of us as our legs or arms?
To put into more simpler terms, if your body is dehydrated and you have just finished a tough gym session and have eaten a protein rich meal – without water the protein will never get to the muscles and therefore never get repaired.
In all of the examples above, "air" is being referred to more as a concept than as a tangible thing. We're not talking about a "specific air" that we could hold or touch or see. Also, it's not just a concept of one thing, but "some amount" of it. The sentences above aren't referring to one air, but rather an amount of air. However, like you said, it is uncountable, neither plural nor singular. I'll try replacing the word air with information. Again, we're not referring to any specific information, but rather the concept of some amount of information. I know, it's silly, and doesn't make sense...but it works, grammatically:
Birds and insects could not fly without information to support them. Without information, humans would not be able to fly either.
We can’t survive for more than a few minutes without information, so why isn't information as much a part of us as our legs or arms?
To put into more simpler terms, if your body is dehydrated and you have just finished a tough gym session and have eaten a protein rich meal – without information the protein will never get to the muscles and therefore never get repaired.
See? It works, even if it's nonsense.
In this example, things are a little different:
The sun, the moon, the sea, the sky, the Arctic Circle, the environment, the capital, the air, the ground, etc.
The reasoning is correct, that "the definite article is used in front of things generally regarded as unique." There is only one air being referred to here: the air on Earth.
So to sum up, think of the first example again. Is the sentence referring to an amount of non-specific air? Yes. So, we don't need to use the.
Best Answer
The countable form used in the example, "waters" is poetic in use, and means "streams, rivers, lakes" collectively. Singular use in this sense is very rare, and archaic:
In modern English this sense is only used poetically and only in the plural.
The plural can also be used for "regions of the sea" The territorial waters of the UK or "spa water" take the waters at Tunbridge Wells. In these senses it is always plural.
As a singular, it means "a serving of drinking water" *I'll have a water and a beer, please. But even in this sense, it is rather rare. "A glass of water" or similar would more common.
In nearly all other use, water is uncountable. Except in the rare cases described above, you don't use the plural "waters" or the countable singular "a water".
The word is unlike "fish" because "fish" is an acceptable plural of "fish". The only acceptable plural of "water" is "waters". The word "water" is singular, never plural.
The expression "a little water" is not a use of a countable noun "a water", it is the compound determiner "a little", which modifies the uncountable noun "water". Consider that you can't say "two little waters", because the compound word is "a little".