Det som ligger i korgen är kex, nötter och lite melon.

Here det som means what or that which.

So:

• Det som ligger i korgen = what is lying in the basket
• More naturally in English: what’s in the basket

This is a very common Swedish pattern:

• det som + clause = what / the thing(s) that ...

The whole phrase acts as the subject of the sentence.

Because vad usually introduces a direct question:

• Vad ligger i korgen? = What is lying in the basket?

But in your sentence, what is in the basket is not a question. It is a noun-like clause that becomes the subject of the sentence. For that, Swedish normally uses det som:

• Det som ligger i korgen är ... = What is in the basket is ...

So a useful shortcut is:

• vad = what?
• det som = what / the thing that

Swedish often uses positional verbs when talking about where things are.

Here ligger is natural because the items are understood as physically resting in the basket.

• ligga = lie, be lying
• stå = stand, be standing
• sitta = sit, be attached/be seated

For loose objects like crackers, nuts, and pieces of melon in a basket, ligger sounds very natural.

English often just says is or are, but Swedish likes to be more specific about physical position.

Yes, both are possible, but they give slightly different nuances.

• Det som ligger i korgen = emphasizes physical placement; very natural for objects resting in a basket
• Det som finns i korgen = more neutral, like what is in the basket / what the basket contains
• Det som är i korgen = possible, but less specific; often sounds plainer

So your original sentence is a good, idiomatic choice for actual things lying in a basket.

i means in.

korgen means the basket:

• korg = basket
• korgen = the basket

Swedish usually adds the definite article to the end of the noun instead of using a separate word like the.

So:

• i korgen = in the basket
• i en korg = in a basket

Because the grammatical subject is not kex, nötter och lite melon. The subject is the whole clause:

• Det som ligger i korgen

That whole clause is treated as one unit, so Swedish uses singular är.

It works the same way in English:

• What is in the basket is crackers, nuts, and some melon

Even though several items are named after is, the subject what is in the basket is singular.

Because Swedish often leaves out articles with indefinite plural nouns and with food items in a general list.

So:

• kex = crackers / biscuits
• nötter = nuts

This sounds like naming the contents, not counting them one by one.

If you wanted to be more exact, you could add quantity words, for example:

• ett kex = one cracker
• några nötter = some nuts

But in your sentence, the bare nouns sound natural.

Because lite melon means some melon or a little melon, not one whole melon.

With food, Swedish often treats something like melon as a mass noun when talking about pieces or an unspecified amount.

So:

• lite melon = some melon
• en melon = a melon, one whole melon

In this sentence, the idea is probably that there are pieces of melon in the basket, not an entire melon.

Because after lite, Swedish normally uses the noun as a mass noun.

So melon here means melon as a substance or food item, not as a countable object.

Compare:

• lite melon = some melon
• en melon = one melon
• några melonbitar = some pieces of melon

So the singular form is exactly what you would expect after lite.

It can be understood as an unspecified amount of crackers/biscuits, and the useful thing to know is that kex often has the same form in singular and plural.

For example:

• ett kex = one cracker
• två kex = two crackers

So in your sentence, kex does not have to show a special plural ending. The context tells you that it refers to crackers as part of the basket’s contents.