Han berättar var nyckeln ligger, men jag hittar den ändå inte.

Because nyckeln is the definite singular form: the key.

• en nyckel = a key
• nyckeln = the key

Swedish often uses the definite ending attached to the noun instead of a separate word like English the. Here it is a specific key that both speakers can identify from context, so nyckeln is the natural form.

Den is the object pronoun referring back to nyckeln.

Since nyckel is a common-gender noun, an en-word, the matching pronoun is den.

• en nyckel → den
• ett hus → det

So jag hittar den ändå inte means that the speaker is replacing nyckeln with den instead of repeating the noun.

Because var is used for location, while vart is used for direction or movement.

In this sentence, the key is already somewhere. The speaker is talking about where it is located, not where it is going.

• Var ligger nyckeln? = Where is the key?
• Vart lägger du nyckeln? = Where are you putting the key?

A good shortcut is:

• var = where something is
• vart = where something is going

Because this is an embedded question, not a direct question.

Direct question: Var ligger nyckeln?

Embedded question after a verb like berättar: Han berättar var nyckeln ligger.

In Swedish, direct questions often have inversion, but embedded questions do not. So the subject nyckeln comes before the verb ligger.

This is similar to English:

• direct: Where is the key?
• embedded: He tells me where the key is.

You do not say He tells me where is the key, and Swedish works the same way here.

Swedish very often uses position verbs where English just uses is.

Ligger literally means lies or is lying, but in everyday Swedish it is often the normal way to describe where an object is located, especially if it is resting somewhere.

So for things like keys, books, papers, and similar objects, ligger is very natural.

Examples:

• Nyckeln ligger på bordet. = The key is on the table.
• Boken ligger i väskan. = The book is in the bag.

Swedish also commonly uses:

• står for things that stand
• sitter for things that sit or are attached/positioned in a certain way

Using är is not always wrong, but ligger sounds more idiomatic here.

Here ändå means something like still, anyway, even so, or nevertheless.

It adds contrast:

• He tells where the key is,
• but I still do not find it.

So ändå shows that the second clause goes against what you might expect. If someone tells you where the key is, you would expect that you can find it. But the speaker cannot, and ändå highlights that mismatch.

In this sentence, ändå inte together gives the feeling of still not or not anyway / not even then.

Because Swedish word order puts inte after the finite verb in main clauses, but short object pronouns like den often come before inte.

That gives this order:

jag + hittar + den + ändå + inte

So jag hittar den ändå inte is natural Swedish.

Compare:

• Jag hittar inte nyckeln. = I do not find the key.
• Jag hittar den inte. = I do not find it.

When the object is a short pronoun like den, it usually comes before inte. Then ändå fits naturally before the negation here: den ändå inte.

Because Swedish can leave the receiver of berättar unstated if it is obvious from context or not important.

A fuller version could be:

• Han berättar för mig var nyckeln ligger.

But Swedish often omits that part if the meaning is already clear. So Han berättar var nyckeln ligger can naturally mean He tells me where the key is, He tells us where the key is, or simply He says where the key is, depending on context.

Also, berätta can mean not only tell a story, but also tell/inform/explain.

Both are possible, but jag hittar den ändå inte is very natural Swedish.

Swedish often uses the plain present tense of hitta where English would use can’t find.

So:

• Jag hittar den inte. = I can’t find it.
• Jag kan inte hitta den. = I cannot find it / I’m unable to find it.

The version without kan is usually more idiomatic in everyday speech when talking about the result of searching. Adding kan can sound a little more explicit about ability, but the sentence you have is perfectly normal and probably the most natural choice here.