Jag hittar ingen nål, men det finns vit tråd i lådan.

Not necessarily. In Swedish, hitta often works this way:

• Jag hittar nyckeln = I find / I’m finding / I can find the key
• Jag hittar inte nyckeln = I can’t find the key

So Jag hittar ingen nål naturally means that the speaker is not succeeding in finding a needle. English often uses can’t here, but Swedish does not always need kan.

You could say Jag kan inte hitta någon nål, but that is a bit more explicit and slightly heavier.

Ingen is the normal negative determiner for a singular en-word noun. It means no or not any.

So:

• ingen nål = no needle / not any needle

By contrast, inte en nål is more emphatic. It can sound like:

• not even one needle
• not a single needle

So in an ordinary neutral sentence, ingen nål is the most natural choice.

Because nål is an en-word and it is singular.

The forms are:

• ingen
  • singular en-word
• inget
  • singular ett-word
• inga
  • plural nouns

Examples:

• ingen nål = no needle
• inget hus = no house
• inga böcker = no books

So the form depends on the gender and number of the noun that follows.

Det finns is a very common Swedish existential expression meaning there is or there are.

So:

• Det finns vit tråd i lådan = There is white thread in the box

The det here is a dummy subject. It does not mean a specific it. It is just part of the construction.

A good way to learn it is as a fixed pattern:

• Det finns ... = there is / there are ...

Examples:

• Det finns kaffe. = There is coffee.
• Det finns två stolar här. = There are two chairs here.

Here tråd is being used like a material or uncountable substance, similar to thread in English.

So:

• vit tråd = white thread

This means some amount of white thread, not one specific thread.

If you said en vit tråd, that would usually mean:

• one white thread
• one strand of white thread

So the version without an article is natural when you mean thread as a material in general.

Because tråd is an en-word and the noun phrase is singular and indefinite.

For Swedish adjective agreement:

• en-word, singular, indefinite → vit
• ett-word, singular, indefinite → vitt
• plural or definite → vita

Compare:

• en vit tråd
• ett vitt hus
• vita trådar
• den vita tråden

So vit tråd is the correct form.

Lådan is the definite singular form of låda, which means box or drawer, depending on context.

So:

• låda = a box / a drawer
• lådan = the box / the drawer

The ending -n here is the definite ending. Since låda already ends in -a, the definite form becomes lådan.

So:

• i lådan = in the box / in the drawer

It refers to a specific box or drawer, not just any one.

Because the meaning is inside the box or drawer.

• i = in, inside
• på = on, on top of, sometimes at

So:

• i lådan = in the box / drawer

If something were on top of the box, then på lådan would make sense.

No. Men is a coordinating conjunction, like but in English. It links two main clauses, and each clause keeps normal main-clause word order.

So in:

• Jag hittar ingen nål, men det finns vit tråd i lådan.

the second clause is still a normal main clause:

• det = subject position
• finns = finite verb

If you move another element to the front, then normal Swedish inversion applies, just as in any main clause. For example:

• ..., men i lådan finns det vit tråd.

That is also possible, though the original sentence is more neutral.

Usually det finns is better here.

Det finns is used to introduce the existence or presence of something:

• Det finns vit tråd i lådan. = There is white thread in the box.

Det är is more often used to identify or describe something already known:

• Det är vit tråd, inte garn.
• Det är lådan jag menar.

So in this sentence, where the point is that white thread is present in the box, det finns is the natural choice.

They do very different jobs:

• hittar comes from hitta = to find
• finns comes from finnas = to exist / to be available / there is

So:

• Jag hittar ingen nål = I am not finding any needle / I can’t find a needle
• det finns vit tråd i lådan = there is white thread in the box

In other words:

• hitta is about what the person succeeds in locating
• finnas is about whether something is present at all

Yes. You can tell because it appears after ingen, which is used with singular en-word nouns.

So:

• ingen nål tells you that nål is an en-word

You can also see this in the indefinite form:

• en nål = a needle

That matters because it affects:

• the article: en nål
• the negative determiner: ingen nål
• adjective agreement with related noun phrases if needed