Q:

Brawl, Quarrel, Argument and Discussion

I was never really sure about the difference between these four, so I went to dictionary.com to check them (http://www.dictionary.com/browse/quarrel?s=t, http://www.dictionary.com/browse/discussion?s=t, http://www.dictionary.com/browse/argument?s=t and http://www.dictionary.com/browse/brawl?s=t).
I'd like to share my impressions to start with. It came to me that there are two pairs of words with closer meanings.
Argument and Discussion
Argument and discussion seem rather civilized, and though they can infer somehow aggressive situations, they tend to be primarily rational and pacific.
However among these, only discussion can be used when a debate is welcome.

They had a very interesting discussion about the pros and cons of the legalization of marijuana.

Seems to be a case where discussion and argument aren't interchangeable. 
Brawl and Quarrel
These are rather aggressive, highly emotional and can easily get physical. I don't see any case we could say a brawl/quarrel was pacific.
The entry for Brawl also gives me the impression Brawl is more of a noisy kind of event than quarrel.
I also looked on Ngram how often they are used in American and British English to check if there was any country preference (https://books.google.com/ngrams/graph?content=Brawl%2CArgument%2Cdiscussion%2Cquarrel&year_start=1800&year_end=2000&corpus=18&smoothing=3&share=&direct_url=t1%3B%2CBrawl%3B%2Cc0%3B.t1%3B%2CArgument%3B%2Cc0%3B.t1%3B%2Cdiscussion%3B%2Cc0%3B.t1%3B%2Cquarrel%3B%2Cc0 and https://books.google.com/ngrams/graph?content=Brawl%2CArgument%2Cdiscussion%2Cquarrel&year_start=1800&year_end=2000&corpus=17&smoothing=3&share=&direct_url=t1%3B%2CBrawl%3B%2Cc0%3B.t1%3B%2CArgument%3B%2Cc0%3B.t1%3B%2Cdiscussion%3B%2Cc0%3B.t1%3B%2Cquarrel%3B%2Cc0), but it seems that in either case discussion is by far the favorite one.
My quations are:

Does the notion above (of dividing them into those groups) make sense?
If so, then what's the difference between each word in each pair? If not, how would you explain the differences among them?
Is discussion really more common than the other three both in AE and in BE?

A:

An argument centers around a disagreement, and can be acrimonious. In a discussion, the disagreement is optional and acrimony is excluded.
A quarrel is a bitter dispute that may not be of a factual nature.  The parties might just not like each other.
A brawl is a physical fight.  Blows are exchanged.

