Мне нужно кое-что купить в супермаркете.

Because this sentence uses an impersonal construction.

In Russian, мне нужно... literally means something like to me, it is necessary... or I need to.... The person who has the need goes into the dative case, so я becomes мне.

So:

• я = I
• мне = to me / for me

This is very common in Russian:

• Мне нужно работать. = I need to work.
• Ему надо идти. = He needs to go.

Нужно means necessary, needed, or more naturally in English, need to.

In this pattern, Russian often uses:

• мне нужно + infinitive
• тебе нужно + infinitive
• нам нужно + infinitive

Examples:

• Мне нужно спать. = I need to sleep.
• Нам нужно поговорить. = We need to talk.

So Мне нужно купить... means I need to buy...

Because after нужно, Russian normally uses the infinitive to say what action is necessary.

So the pattern is:

[person in dative] + нужно + infinitive

Here:

• мне = to me
• нужно = necessary / need to
• купить = to buy

So the structure is basically:

I need to buy...

This is about aspect.

• купить = perfective
• покупать = imperfective

In this sentence, купить is used because the speaker means to buy something as a completed result. The focus is on getting the purchase done.

So Мне нужно кое-что купить means something like:

• I need to buy a few things
• I need to get something bought

If you said покупать, it would sound more like the process or repeated action of buying, which is less natural here.

A learner-friendly rule: When you mean I need to do X and finish it, Russian often prefers the perfective infinitive.

Кое-что means something, a few things, or some stuff, depending on context.

It suggests that the speaker has some specific but unspecified thing(s) in mind.

So in this sentence, it gives the idea:

• I need to buy something
• I need to buy a few things

It is a bit vague, but not completely random.

This is a very common question.

Both can often be translated as something, but they are not exactly the same.

что-то

Usually means something, often unknown, indefinite, or unspecified.

• Я что-то слышу. = I hear something.
• Нужно что-то сделать. = We need to do something.

кое-что

Often suggests some particular thing(s) that the speaker has in mind, but does not name directly.

• Я хочу тебе кое-что показать. = I want to show you something.
• Мне нужно кое-что купить. = I need to buy a few things / something in particular.

So кое-что can feel a little more like: I have something specific in mind, but I am not spelling it out.

Because words with кое- are usually written with a hyphen in Russian.

Examples:

• кое-что
• кое-кто
• кое-какой
• кое-где

This is just a spelling rule you need to learn.

A useful note: If there is a preposition inside the expression, the spelling changes:

• кое с кем
• кое у кого

But in кое-что, there is no preposition, so you use the hyphen.

Because here в means in / at, showing the location where the buying happens.

After в, Russian can use different cases depending on meaning:

Location: in / at

Use the prepositional case:

• в супермаркете = in the supermarket

Direction: into / to

Use the accusative case:

• в супермаркет = into the supermarket

So compare:

• Мне нужно кое-что купить в супермаркете. = I need to buy something in/at the supermarket.
• Мне нужно идти в супермаркет. = I need to go to the supermarket.

In your sentence, the supermarket is the place where the action happens, not the destination of movement.

Супермаркете is in the prepositional case.

The dictionary form is супермаркет. After в when it means location, Russian uses the prepositional:

• супермаркет → в супермаркете

This ending is very typical for many masculine nouns:

• в магазине
• в банке
• в супермаркете

So the ending -е is there because the noun is in the prepositional case after в meaning location.

Yes. Russian word order is more flexible than English word order.

The neutral order here is:

Мне нужно кое-что купить в супермаркете.

But other orders are possible if you want to emphasize something:

• В супермаркете мне нужно кое-что купить.
  Emphasis on in the supermarket
• Кое-что мне нужно купить в супермаркете.
  Emphasis on some things

Even though the order can change, the original version sounds natural and neutral.

Yes. That is perfectly natural.

Both надо and нужно can mean need to.

General tendency:

• надо often sounds a bit more conversational
• нужно can sound a bit more neutral or slightly more formal

But in everyday speech, both are very common, and in this sentence either one works well.

Not in the same way as in English.

This is an impersonal sentence. Russian does not need a subject like I in the nominative here. Instead, the person affected is shown in the dative:

• мне = to me

And нужно functions as the impersonal predicate.

So the sentence does not literally say I need in the same grammatical way English does. It is more like:

To me, it is necessary to buy something in the supermarket.

That is why it feels different from English grammar.

Yes, very often it can.

Grammatically, что is singular, but кое-что is often used in a loose, everyday way to mean:

• something
• a few things
• some stuff

So in a shopping context, Мне нужно кое-что купить often sounds like the speaker has a few items to buy, not necessarily just one single item.

Context decides how broad it is.

It would change the meaning a little.

• кое-что = some specific thing(s), not named
• что-нибудь = anything / something, no specific item in mind

So:

• Мне нужно кое-что купить в супермаркете.
  I have some particular things in mind.

• Мне нужно что-нибудь купить в супермаркете.
  I need to buy something or other; almost anything would do.

That is why кое-что is a better choice if the speaker already knows roughly what they need.

A natural pronunciation would usually stress the meaningful words, especially нужно, кое-что, купить, or супермаркете, depending on what you want to emphasize.

A neutral rhythm is roughly:

Мне нужно кое-что купить в супермаркете.

A few pronunciation notes:

• мне is one syllable: sounds like mnye
• нужно is roughly NOOZH-na
• кое-что has the stress on что
• купить has stress on the last syllable: ku-PEET'
• супермаркете has stress on мар: super-MAR-ke-tye

You do not need to pronounce every word with equal force. Russian usually has one or two stronger stresses in the sentence, with the rest reduced more than in English.