Er ligt een brief op het bureau, en mijn adres staat daarop.

Here er is an existential word, used when introducing the existence or presence of something. In English, we often use there is / there are for this.

So:

• Er ligt een brief op het bureau. = There is a letter on the desk.

This er often appears with indefinite nouns such as een brief. It helps present new information.

Compare:

• Er ligt een brief op het bureau. = There is a letter on the desk.
• De brief ligt op het bureau. = The letter is on the desk.

The second one is about a specific letter already known in the conversation, while the first one introduces a letter.

Dutch often uses verbs of position where English simply uses to be.

Here, liggen means to lie and is used for things that are lying flat or are simply located somewhere in a resting position.

So:

• De brief ligt op het bureau. = The letter is lying on the desk / The letter is on the desk.

Dutch commonly distinguishes:

• liggen for things lying
• staan for things standing
• zitten for things being located in, on, or attached in certain ways

English usually just says is.

Een means a/an, while de or het can mean the.

Because the sentence is introducing the letter for the first time, Dutch uses een brief:

• Er ligt een brief op het bureau. = There is a letter on the desk.

If the speaker meant a specific letter already known to both speaker and listener, they would more likely say:

• De brief ligt op het bureau. = The letter is on the desk.

In Dutch, every noun has a grammatical article: de or het.

Bureau is a het-word, so:

• het bureau = the desk

That is why the phrase is:

• op het bureau = on the desk

You just have to learn whether a noun takes de or het. There are some patterns, but many learners simply memorize nouns together with their article.

Daarop means on it, on that, or on there, depending on context.

It is made from:

• daar = there / that
• op = on

So:

• mijn adres staat daarop = my address is on it

Instead of repeating op het bureau, Dutch uses daarop to refer back to something already mentioned. In this sentence, daarop refers to een brief, not to het bureau.

That is important:

• The letter is on the desk
• The address is on the letter

So daarop means on that letter

Because of meaning and context.

The previous clause says:

• Er ligt een brief op het bureau = There is a letter on the desk

Then:

• mijn adres staat daarop = my address is on it

Logically, an address can be written on a letter, not normally on a desk, so daarop naturally refers to brief.

In Dutch, pronoun reference is often resolved by context, just as it is in English.

Dutch often uses staan for written or printed information.

So if text appears on paper, a sign, a page, a label, or a screen, Dutch often says it stands there:

• Mijn naam staat op de lijst. = My name is on the list.
• Het adres staat op de envelop. = The address is on the envelope.
• Wat staat er in de brief? = What does the letter say? / What is written in the letter?

This may feel strange to English speakers, but it is very normal in Dutch.

The basic structure is:

• Er
  • verb
    • subject
      • other information

So:

• Er = existential placeholder
• ligt = verb
• een brief = subject
• op het bureau = place

This is a very common Dutch pattern when introducing something:

• Er staat een fles op tafel.
• Er zit een fout in de tekst.
• Er ligt een sleutel onder de stoel.

English speakers may expect the subject earlier, but after existential er, Dutch usually places the verb before the noun phrase.

Both are possible, but they have slightly different emphasis.

• Mijn adres staat daarop. = neutral statement; focus starts with my address
• Daarop staat mijn adres. = more emphasis on on that / on it

Dutch allows some flexibility because of verb-second word order. The conjugated verb must be in the second position in a main clause:

• Mijn adres | staat | daarop
• Daarop | staat | mijn adres

Both are grammatical. The version in your sentence is simply the more neutral one in this context.

Because Dutch often combines a preposition with daar-, hier-, or waar- into one word.

Examples:

• daarop = on it / on that
• daarin = in it / in that
• daaronder = under it / under that
• waarop = on what / on which
• hierop = on this / on it here

English uses separate words, but Dutch frequently merges them.

One important note: this is especially common when referring to things, not people. For people, Dutch usually uses a different structure:

• Ik wacht op hem. = I’m waiting for him.
• not Ik wacht daarop if you mean a person

Not in this exact sentence, unless the meaning changes.

• mijn adres = my address
• zijn adres = his address

So the grammar is the same, but the reference changes.

This is worth noticing because Dutch possessive adjectives are straightforward:

• mijn = my
• jouw / je = your
• zijn = his
• haar = her
• ons / onze = our

The comma is optional in many cases like this, but it is often used when two main clauses are joined and the sentence is a bit longer.

Here you have two full clauses:

• Er ligt een brief op het bureau
• mijn adres staat daarop

Joining them with en is perfectly normal, and the comma helps readability.

So:

• Er ligt een brief op het bureau en mijn adres staat daarop.
• Er ligt een brief op het bureau, en mijn adres staat daarop.

Both are acceptable, though style preferences may differ.

Yes.

Because Dutch main clauses follow the verb-second rule, if you move daarop to the front, the verb must still remain second:

• Daarop staat mijn adres.

That version is very natural too. It puts a bit more emphasis on the location on it / on that.

So you can compare:

• Mijn adres staat daarop. = neutral
• Daarop staat mijn adres. = slightly more focus on there/on it

Yes, bureau can mean more than one thing depending on context.

Most commonly:

• het bureau = desk

But it can also mean:

• office
• agency
• department

For example:

• Ik zit aan mijn bureau. = I’m sitting at my desk.
• Hij werkt op een advocatenbureau. = He works at a law office / legal agency.

In your sentence, op het bureau clearly means on the desk.