Du er den eneste.

Yes. Du is the normal singular you in Danish.

A few useful comparisons:

• du = singular you
• I = plural you
• De = formal you (now uncommon and quite formal/old-fashioned)

So Du er den eneste is speaking to one person in the normal modern way.

Because Danish verbs do not change by person the way English verbs sometimes do.

With at være = to be, the present tense is er for everyone:

• jeg er = I am
• du er = you are
• han/hun er = he/she is
• vi er = we are
• I er = you are
• de er = they are

So er is simply the present tense form of at være.

Den eneste means the only one.

Danish often uses:

• den/det/de
  • adjective

when the noun is definite or understood from context.

Here, the noun is left out, but it is understood. You can think of it as something like:

• Du er den eneste person = You are the only person

When the noun is omitted, den eneste still works by itself and means the only one.

So den is there because this is a definite phrase, not just the adjective by itself.

It is an adjective, but here it is being used substantively, meaning it stands in place of a noun.

That is very common in Danish.

Compare:

• Du er den eneste = You are the only one
• Du er den eneste person = You are the only person

In both cases, eneste is still describing something; in the first sentence, the noun is just left unstated.

Because den, det, and de depend on gender and number.

Here is the pattern:

• den eneste = common gender singular
• det eneste = neuter singular
• de eneste = plural

In Du er den eneste, the understood noun is usually something like person, which is common gender, so den is used.

Examples:

• Du er den eneste = You are the only one
• Det er det eneste = That is the only thing / the only one
• I er de eneste = You are the only ones

Normally, no. In this sentence, eneste needs den.

So:

• Du er den eneste = correct
• Du er eneste = not natural/incorrect in this meaning

If you mean you are alone, Danish uses a different word:

• Du er alene = You are alone

That is a different idea from you are the only one.

No.

• Du er den eneste = You are the only one
• Du er alene = You are alone / by yourself

These can overlap in some situations, but they are not the same.

For example:

• If only one person agrees with something, you can say Du er den eneste.
• If someone is physically by themselves, you can say Du er alene.

You move the verb before the subject:

• Er du den eneste? = Are you the only one?

This is a very common Danish pattern in main clause questions:

• statement: Du er den eneste
• question: Er du den eneste?

A careful pronunciation is approximately:

• Du er den eneste
• IPA: /du ˈɛɐ̯ dɛn ˈeːnəsdə/

A rough English-style approximation could be:

• doo air den AY-nuh-stuh

But that is only approximate. A few notes:

• du has a long u sound
• er is often reduced in normal speech
• eneste has stress on the first syllable

As with many Danish phrases, natural spoken pronunciation is often more reduced than the careful written form suggests.