Not a teacher
I think in these sentences the writers mean each person have a coffee/beer. In the first two sentences, maybe "both" was cut down.
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)?
Not a teacher
I think in these sentences the writers mean each person have a coffee/beer. In the first two sentences, maybe "both" was cut down.
My understanding is this:
1. ambigious, but most likely means this:
We had a coffee each. -- two coffees altogether
2. We ordered two coffees. -- the waiter brought two coffees on his plate
We ordered a coffee -- one coffee on the plate, but it is also possible there were two (the waiter is bad at maths).
3. Let us have a beer. -- Most likely means this: each gets one.
If you are uncertain in real situations, ask the speaker how many (s)he means.
I'd say that "We met for coffee" or "We had coffee together" or "Let's go for coffee" is just as common where I'm from.
Rarely do we need to specific that we each had one cup, and no more. (We had a coffee.)
In fact, even if you do say something like "We met for a quick cup of coffee," it doesn't imply that the mug was never refilled at some point.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.