Learn English – How to know whether “over” means more than or during

New Year is the first day of the year, which for the Gregorian calendar is January 1. In most countries, that is a holiday.

The sentence shown by the OALD ("We are away over the New Year.") implies "We will return after the New Year." Rephrasing this sentence to use be away, it becomes "We are away until after the New Year." This is not different from the following sentences.

They didn't reach the border until after dark.

He refused to comment until after the trial.

You cannot legally take possession of the property until after the contract is signed.

Until means "up to the point in time or the event mentioned"; in "until after the New Year" the point in time is "after the New Year."

Your mother tongue, also known as first language or native language, is the language you grow up speaking at home. Most people have one native language and may acquire second languages at various levels of fluency.

A first language (also native language, mother tongue, arterial language, or L1) is the language or are the languages a person has learned from birth or within the critical period, or that a person speaks the best and so is often the basis for sociolinguistic identity[citation needed]. In some countries, the terms native language or mother tongue refer to the language of one's ethnic group rather than one's first language. Children brought up speaking more than one language can have more than one native language, and be bilingual.

By contrast, a second language is any language that one speaks other than one's first language. [emphasis added]

There are several principles that separate a "native language" from a second language:

The article titled “The Native Speaker: An Achievable Model?” published by the Asian EFL Journal states that there are six general principles that relate to the definition of "native speaker". These principles, according to the study, are typically accepted by language experts across the scientific field. A native speaker is defined according to the guidelines that:

1. The individual acquired the language in early childhood
2. The individual has intuitive knowledge of the language
3. The individual is able to produce fluent, spontaneous discourse
4. The individual is competent in communication
5. The individual identifies with or is identified by a language community
6. The individual does have a dialect accent (include official dialect)

It's slightly ambiguous from your question but I'm going to assume that Katy learned Japanese and Thai much later on than she learned English.

In your example, Katy's native language (mother tongue) is English and she has two second languages that she is fluent in, Japanese and Thai. This must be the case as English is the only language that meets all six of the above requirements.

For the purposes of your example, this is your answer, and no other information is necessary, since Katy did not learn the other two languages as a child.

As noted in the Wikipedia article, it is possible, should a child have bilingual parents, for that child to grow up speaking more than one language, and, thus have multiple "mother tongues".

Sometimes the term mother tongue or mother language is used for the language that a person learned as a child at home (usually from their parents). Children growing up in bilingual homes can, according to this definition, have more than one mother tongue or native language.

For example, many people in Quebec, Canada speak both French and English:

A considerable number of Quebec residents consider themselves to be bilingual in French and English. In Quebec, about 42.6 percent of the population (3,328,725 people) report knowing both languages; this is the highest proportion of bilinguals of any Canadian province

If a couple has a child and chooses to speak both English and French in the home, that child would have two native languages.

Some regions have specific definitions for the term "mother tongue" that does not agree with what has been stated above, and are worth mentioning:

In the context of population censuses conducted on the Canadian population, Statistics Canada defines mother tongue as "the first language learned at home in childhood and still understood by the individual at the time of the census."

So this definition allows for only one "mother tongue".

Additionally, some groups refer to their ethnic group's language which they may or may not know as their "mother tongue":

In some countries, such as Kenya, India, and various East Asian countries, "mother language" or "native language" is used to indicate the language of one's ethnic group, in both common and journalistic parlance (e.g. "I have no apologies for not learning my mother tongue"), rather than one's first language.

Also, there is no requirement that a person still speak their "mother tongue" or be literate in it:

It is quite possible that the first language learned is no longer a speaker's dominant language. This includes young immigrant children, whose families have moved to a new linguistic environment, as well as people who learned their mother tongue as a young child at home (rather than the language of the majority of the community), who may have lost, in part or in totality, the language they first acquired (see language attrition).

As an example, say a child (an orphan) was born in Russia and lived there until the age of five, speaking only Russian. At that point, the child was adopted by American parents and stopped speaking Russian entirely, switching to English, and no longer understands Russian at all.

I'd argue the child's "mother tongue" is Russian but they are a native speaker of English.

Some other interesting tidbits from the article:

According to Ivan Illich [an Austrian philosopher and Roman Catholic priest], the term "mother tongue" was first used by Catholic monks to designate a particular language they used, instead of Latin, when they are "speaking from the pulpit". That is, the "holy mother the Church" introduced this term and colonies inherited it from the Christianity as a part of their colonial legacy, thanks to the effort made by foreign missionaries in the transitional period of switching over from 18th-century Mercantile Capitalism to 19th-century Industrial Capitalism in India.

This is important as it shows the general use of "mother" as in "motherland", or the "land of one's birth" so "mother tongue" is the "language of one's birth". Not specifically relating to the language that only your mother speaks, excluding whatever (possibly different) language your father might speak.