raisyuu no kayou ni atarasii arubaito no mensetu ga arimasu.

の here links two nouns in a possessive/associative way, making “Tuesday of next week”.

• 来週 = next week
• 火曜 = Tuesday
• 来週の火曜 literally = “next week’s Tuesday” → natural English: “next Tuesday” (where “next” is relative to the week).

In general, A の B can be:

• possession: 私の本 = my book
• description/association: 日本の会社 = Japanese company
• time/period relationship: 来週の火曜 = Tuesday of next week

You’ll often see and hear both:

• 来週の火曜（に）
• 来週火曜（に）

When used in front of time words like days, の can be dropped in casual speech without changing the meaning.

• With の: slightly clearer, a bit more “textbook” / neutral.
• Without の: common in spoken Japanese, especially when spoken quickly.

So yes, 来週火曜に新しいアルバイトの面接があります is also fine in everyday Japanese.

They both mean Tuesday.

• 火曜日 (かようび) is the full form, used in textbooks, formal writing, schedules, etc.
• 火曜 (かよう) is an abbreviated form, very common in conversation, ads, timetables, TV guides, etc.

Using 火曜 instead of 火曜日 doesn’t change the meaning. It’s a bit like saying “Tues” instead of “Tuesday” in English, but in Japanese the shortened forms are very standard and not particularly informal.

に marks a specific point in time when something happens.

• 火曜に = on Tuesday
• 来週の火曜に = (on) next Tuesday

In many cases with time expressions, に is optional:

• 来週の火曜、新しいアルバイトの面接があります。
• 来週の火曜に、新しいアルバイトの面接があります。

Both are acceptable. に tends to be used more:

• when you want to be clear or formal
• when the time phrase is long or could be ambiguous
  But dropping it is very common in speech.

However, に is required in many other uses (e.g. marking destinations, indirect objects), so here you can think: “Recommended but often omitted in casual speech.”

来週 is directly connected to 火曜 by の, forming 来週の火曜. Within that phrase:

• 来週 modifies 火曜 (next week’s Tuesday),
• 火曜 is the main noun of the phrase,
• and に attaches to that main noun: 来週の火曜に

If you wanted 来週 to be an independent time expression (not modifying 火曜), you could say:

• 来週、火曜に新しいアルバイトの面接があります。
  (Next week, on Tuesday, I have an interview for a new part-time job.)

In that structure, 来週 stands alone as a time adverb at the start of the sentence and doesn’t need a particle either. Basic rule: many time words can appear without a particle when they function as time adverbs.

新しい is an adjective meaning new, and it modifies アルバイト:

• 新しいアルバイト = a new part-time job

Then 新しいアルバイト as a whole modifies 面接 via の:

• 新しいアルバイトの面接 = interview for a new part-time job

So the structure is:

• 新しい → describes アルバイト
• 新しいアルバイト → describes 面接 with の

アルバイト is written in katakana because it’s a loanword from German (Arbeit, “work”). In Japanese, katakana is used for:

• foreign loanwords (e.g. コンピューター computer)
• foreign names
• some onomatopoeia and emphasis

In modern Japanese, アルバイト doesn’t mean just “work” in general; it specifically means:

• part-time job, often held by students or people working fewer hours.

You might also see:

• バイト (shortened form) in casual speech.
• パート (from “part-time” in English), often used more for housewives or longer-term part-time positions, but the distinction is fuzzy and context-dependent.

In this sentence, 新しいアルバイト clearly means a new part-time job.

Here の links two nouns, making 面接 (interview) “belong to” or “be about” the part-time job:

• アルバイトの面接 = interview for a part-time job

So A の B often corresponds to “B for A” or “B of A” in English when A is the “target” or “topic” of B:

• 仕事の面接 = job interview
• 入学の面接 = entrance interview
• アルバイトの面接 = part-time job interview

が marks the subject of the verb ある (to exist / there is). The subject here is:

• 新しいアルバイトの面接 (the new part-time job interview)

So:

• 新しいアルバイトの面接が あります。
  = There is a new part-time job interview.
  / I have an interview for a new part-time job. (natural translation)

が is often used to introduce or highlight something that exists, appears, or happens, especially with verbs like:

• ある / いる (to exist)
• わかる (to understand)
• 見える / 聞こえる (can be seen / heard)

Japanese often talks about events and possessions using existence verbs like ある.

• 面接があります。 literally = There is an interview.
• But contextually, it usually means I have an interview (if you’re speaking about yourself).

Japanese frequently omits the subject when it’s obvious from context:

• Full version would be something like:
  私は来週の火曜に新しいアルバイトの面接があります。
  = As for me, there is an interview for a new part-time job next Tuesday.

But 私は is dropped because it’s clear that you’re talking about yourself. So:

• 来週の火曜に新しいアルバイトの面接があります。
  is the natural, concise way to say “I have a new part-time job interview next Tuesday.”

ある is itself a verb, not an adjective or noun, so it doesn’t need です after it.

• Dictionary form: ある
• Polite non-past form: あります

You don’t say ありますです; that would be ungrammatical in standard Japanese.
The sentence’s verb is simply:

• あります = there is / (I) have (for inanimate things and events)

Compare:

• 本がある。 → plain
• 本があります。 → polite

Yes, that sentence is also grammatically correct and natural:

• 来週の火曜に新しいアルバイトの面接があります。
• 新しいアルバイトの面接が来週の火曜にあります。

Both mean the same thing. Japanese word order is flexible as long as:

• Particles stay attached to the right words.
• The verb (here あります) usually comes at the end.

Placing the time expression at the beginning is very common, because it sets the time frame first. Putting it later can lightly emphasize the thing that comes first (here: the interview itself).

You mainly change the intonation and/or add か at the end:

• 来週の火曜に新しいアルバイトの面接がありますか。
  = Do you have a new part-time job interview next Tuesday?

Spoken, you might also just raise your voice at the end:

• 来週の火曜に新しいアルバイトの面接がある？ (casual)
  = You have a job interview next Tuesday?

Key points:

• Add か for a polite question.
• In casual speech, dropping か and just using rising intonation is very common.