Is politeness the right term to describe **連用形+ます** inflection? Should it be
always referred as **formal** instead of **polite** , and **informal** instead
of **plain**?

Politeness is the listener's interpretation of the opponent's communication
style. Words in Japanese inflect to project different levels of formality, how
can they be polite or impolite by themselves? A speaker can use very formal
language and at the same time be very impolite to the listener, e.g. employing
sarcasm or certain body language.
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terminology
Politeness vs. Formality
Your question: A speaker can use very formal language and at the same time be
very impolite to the listener, e.g. employing sarcasm or certain body
language.

Yes off course! I believe it doesn't depend on the language.

Such situaiton we call "慇懃無礼 (a feigned politeness)" in Japanese.
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2017-01-17T03:59:54.837
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Japanese has this term: 社交{しゃこう}辞令{じれい}

In English, that may be defined as "diplomatic way of putting things" ([社交辞令
on Jisho.org](http://jisho.org/word/%E7%A4%BE%E4%BA%A4%E8%BE%9E%E4%BB%A4)) or
"diplomatic wording" (direct translation by looking up each word in
dictionaries).

**How to discover**

The term `社交辞令` is not easy to discover when looking into bilingual
dictionaries, regardless of searching from either languages.

  * English-Japanese dictionaries: The term will _not_ be found when looking up using any of these keywords: diplomatic, polite, formal.

  * Japanese-English dictionaries: The term may _not_ be found when looking up using either word `しゃこう 社交` or `じれい 辞令`.

  * Online Japanese dictionary: Many words found in result and `社交辞令` is included i.e. [search result for "diplomatic" on Jisho.org](http://jisho.org/search/diplomatic).

The term `社交辞令` is less likely used in conversation for some reason that I may
aware (but decided not to mention here). I have only heard this term several
times on Japanese TV documentaries or variety show that features interviewer
meeting Japanese people on street.

**Alternate translations**

In English, the word 'diplomatic' mainly refers to diplomatic relation between
countries but this can be extended to relation between people.

> ADJECTIVE [...] Having or showing an ability to deal with people in a
> sensitive and tactful way. -- [Oxford
> Dictionaries](https://en.oxforddictionaries.com/definition/diplomatic)

Note that online dictionary might include other words, such as "polite" or
"lip service" as translation for the term `社交辞令`. However, being diplomatic
does not necessary mean polite, impolite or rude or anything in particular.

Above all, I'm almost certain that this term is most appropriate to describe
the generic politeness and formality that doesn't necessary mean polite or
otherwise impolite by itself.
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