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May I ask you the following questions?

1. We had a coffee.
Does this mean we shared a single cup of coffee or we each had a cup of coffee?
If it is a big pizza instead of a coffee, I think it means that we ordered a single pizza pie to share with.

2. We ordered a coffee.
A similar question. Did we order a single coffee or order a single coffee each?

3. Let's have a beer.
Is this okay? Does it mean that we are going to have a beer each (and not going to share a beer)?
Comments  
You must use common sense, just as you do in your own language.
Mister MicawberYou must use common sense, just as you do in your own language.

The problem is, as you probably know, almost all Japanese nouns are uncountable.
Students: Are you brave enough to let our tutors analyse your pronunciation?
These are all acceptable in the US (rules or no rules):

You can buy an ice cream cone, not an ice cream.

You can buy me a beer, very rarely "a bottle of beer".

Can you get me a bottle of water? not a water. (although you'd hear "please get me a water..")

I'll buy you a Coke/ soda if you let me use your phone to call my mom.

A cup of coffee/tea, not a coffee.

A glass/bottle of water, not a water.

Two cubes of sugar in your coffee? (if you are on a date and you try to help her with her coffee)
Snappy1. We had a coffee.

2. We ordered a coffee.
3. Let's have a beer.
In all three cases, you can safely assume that each is understood after the subject. The amounts usually served of coffee and beer are not so enormous that it is customary to share.

We each had; We each ordered; Let's each have.

Contrast:

We had a turkey at Thanksgiving dinner.

Each person could not possibly eat a whole turkey. Here one would not assume that "We each had a turkey".

CJ
The problem is, as you probably know, almost all Japanese nouns are uncountable.
That is not relevant to what you asked, and not really true anyway, Snappy; Japanese merely lacks the article.

Students: We have free audio pronunciation exercises.
MM is right. If, for whatever reason, common sense doesn't work, ask "Did you each get a coffee?"