In the dialect called "standard English", an is used before words that start with vowel sounds. This includes the word answer. The use of a answer is not in accordance with standard English.
It is possible that one, or even both, of the usages that you have found of a answer is a typographical error (or 'typo') for an answer. However, you should also know that in some dialects of English other than "standard English," the use of a before a word that begins with a vowel sound is acceptable. This is true in dialects found in both the USA and the UK.
For example, see the ELU Question A tendency to use “a” in place of “an” in American English.
For usage in the cosmopolitan city of London, England, see A Corpus-Based Sociolinguistic Study of Indefinite Article Forms in London English (brought to my attention by snailplane), which "reports on the analysis of the use of indefinite article forms (a/an) in front of vowel sounds in spoken London English" (my emphasis).
My point is that some native speakers do use a and not an before words that start with a vowel sound. This is a legitimate variation, and not a "typo." The only, actual, universal "rule" regarding the use of a / an is what native speakers feel comfortable saying. One or two hundred years ago, an university was the norm; today it is a university. Even today, some speakers say an hundred.
So, you shouldn't be surprised when you come across such usages as
The problem is that Trump isn’t enough of a answer-avoiding politician, said Carson.
(The Guardian)
They may be a typo, or they may be an accurate written representation of what the person would have said in spoken English.
You have asked specifically about a answer, but this usage is the same as a before other words, such as a apple. (It is easy to find examples in Google Books of a apple; it is much more time consuming to find additional examples (besides the two you found) of a answer because of the connection between the letter a and answer keys.)
The following piece mentions that a apple is found in AAVE (African American Vernacular English).
Evaluation of a Code-switching Composition Curriculum for Students who Speak ...
Again, see The Adventures of Harry Richmond (Complete) (1924) for three instances of a apple and Such Was the Season (2003) for two more examples of a apple.
This is authentic English, which often does not conform to the dialect called "standard English.
Best Answer
In this sentence:
the idea is that this particular sound can be identified as the sound of an instance of rain which is heavy relative to other rainfalls. The indefinite article specifies "instance" or "generic/paradigmatic instance".
So the sentence is not about the ongoingness of the rain, but the sort of rain the rain is.
Compare:
versus
In the first sentence, the type of bark is being identified: it belongs to a small breed of dog. In the second sentence, the ongoing/repetitive aspect of the bark is being emphasized.