Argthtjtr

The usage of singular and plural has always been confusing for me.

I often see sentences like these

1. People are using cell phones.


2. People are using a cell phone.

Does the first sentence mean everyone has a phone and they are all using their own?
Does the second sentence mean they are sharing one cell phone?

If I see a group of people holding a cell phone in their hand(s), <- even this is confusing for me, should I use the first sentence then?

Another example: you see two men, and both of them are carrying a bag. Which sentence should I say/use?

3. They are carrying backpacks


4. They are carrying a backpack

Could you please make it clear for me?

This aspect of grammar is called the distributive plural. Swan in Practical English Usage (p530) has the following discussion:

Singular and plural: distributive plural

1. people doing the same thing

To talk about several people doing the same thing, English usually
prefers a plural noun for a repeated idea.

• Tell the kids to bring raincoats to school tomorrow.




• (More natural than Tell the kids to bring a raincoat ...)

Plural forms are almost always used in this case if there are
possessives.

• 
  Tell the children to blow their noses. (not ... to blow their nose.)


• 
  Six people lost their lives in the accident.

Quirk et al. in A Comprehensive Grammar of the English Language (p768) list two similar examples:

• Have you all brought your cameras? [Each has a camera.]




• Hand in your papers next Monday. [Each has to hand in one paper.]

and agree with Swan that "... the distributive plural is the norm ...".

But the CGEL goes on to state that:

... the distributive singular may also be used to focus on individual
instances. We therefore often have a number choice.

• Some children have understanding fathers / an understanding father.




• We all have good appetites / a good appetite.

The CGEL concludes its discussion as follows:

The singular is sometimes used to avoid ambiguity:

• Students were asked to name their favorite sport.

The singular makes it clear that only one sport was to be named. Similarly:

• Children must be accompanied by a parent.

Turning to the OP's example, the speaker has a 'number choice'. While, according to Swan and Quirk, the plural is the more usual form (People are using cell phones), the singular (People are using a cell phone) can also be used 'to focus on individual instances'.

As for the recipient of the message, their world-knowledge will most likely lead them to interpret both sentences identically, namely that each person is using his or her own single phone. People don't usually use more than one phone at a time, and people even less usually jointly and simultaneously use a single phone.

The same reasoning applies to the backpack example. Our experience of the world tells us that people almost always carry a single backpack and almost never share the carrying of a single backpack.

It is incumbent, therefore, on the maker of the message to anticipate when our real-world experience may lead us to the wrong interpretation or when the message is inherently ambiguous and a correct interpretation is important. In both such cases, the message needs to be phrased in such a way as to be clear to the recipient how many of the items are involved for each of the people.

For example:

• Two people and one backpack: They are carrying a backpack between
  them.




• People, all using more than one phone: People are using each of their
  phones.

The original post includes 5 inter-related questions and 2 split examples... Making this tricky usage very hard to solve with examples.

So here is a principle: "If the occurrence described is generalized, then the plurality of objects is also generalized."

Here is an example of a specific description:
"Right now people in the next room are using a phone."

Since the description is specific to 1 occurrence, the plural "people" and singular "phone" should be treated literally.
There is 1 occurrence of multiple people using 1 phone.

Here is an example of a general description:
"Once you needed a computer to go online, but now people are using cell phones."

Since the situation is generalized the details involved are also generalized.
The speaker references both plural "people" and plural "cell phones" emphasizing the fact that this description is not specific. They don't care about the exact relationship between number of people and number of phones.

For reading and listening to English watch for "specific or general" indicators. Not everyone will use them consistently, but it is common enough to serve as a guideline.

For speaking or writing, make it a goal to use good "specific & literal" or "general and non-literal" indicators:

"I saw 2 men, each carrying a backpack." { specific & literal, each man has a backpack}

"I saw 2 men carrying a backpack." { specific & literal, without a clarifying word like "each" this means they are both holding the same backpack. }

"I have often seen men carrying backpacks" {general & non-literal, there was more than one occasion, there was more than 1 man, there was more than 1 backpack...}

So, this is difficult.

Imagine you are reading a recounting of a historical event.

"The Romans are armed with a short sword known as a gladius which they use to great effect."

Obviously the Roman army has more than one sword but we are using the singular of Gladius here. But there is no way to be certain if that other than context.

I would recommend avoiding phrasing like this and using context to decipher it when you come across it. It is grammatically correct however.