Ich habe heute eine Wohnungsanzeige gelesen und sofort dem Makler geschrieben.

This is the Perfekt tense, which is very common in everyday German for completed past actions.

So:

Ich habe heute eine Wohnungsanzeige gelesen ...
literally has the structure I have today an apartment ad read, but in natural English it is usually just I read an apartment listing today ...

In spoken German, Perfekt is often preferred over Präteritum for ordinary past events. A more literary or narrative version could be:

Ich las heute eine Wohnungsanzeige und schrieb sofort dem Makler.

That is grammatically correct, but it sounds more like written storytelling than normal conversation.

Because both verbs share the same subject (ich) and the same auxiliary verb (habe).

The sentence really means:

Ich habe heute eine Wohnungsanzeige gelesen und ich habe sofort dem Makler geschrieben.

German normally avoids repeating the auxiliary when it is the same for both parts. That makes the sentence more natural and less repetitive.

You could say:

Ich habe heute eine Wohnungsanzeige gelesen und habe sofort dem Makler geschrieben.

That is also correct, but the shorter version is smoother.

These are different cases because the two nouns have different roles in the sentence.

• eine Wohnungsanzeige is the thing being read, so it is the direct object and takes the accusative
• dem Makler is the person receiving the writing, so it is the indirect object and takes the dative

So:

• eine Wohnungsanzeige gelesen = read an apartment listing
• dem Makler geschrieben = wrote to the agent

A useful pattern is:

• etwas lesen → to read something
• jemandem schreiben → to write to someone

That is just how German works with this verb.

German often says:

jemandem schreiben = write to someone

So the person is in the dative, with no preposition needed.

Examples:

• Ich schreibe meiner Freundin.
• Er hat dem Lehrer geschrieben.

English needs to, but German usually does not.

If you want to mention what was written, you can add a direct object:

• Ich habe dem Makler eine E-Mail geschrieben.
• Ich habe dem Makler eine Nachricht geschrieben.

Wohnungsanzeige is a compound noun.

It is made from:

• Wohnung = apartment / flat
• Anzeige = ad / advertisement / listing

So Wohnungsanzeige means an apartment advertisement or apartment listing.

German forms compound nouns very freely. The last part usually tells you the basic category of the word. Here the last part is Anzeige, so the whole word is a kind of ad.

That also determines the gender:

• die Anzeige
• therefore die Wohnungsanzeige

In this context, Makler means a real-estate agent or broker, someone handling the apartment listing.

Because the sentence mentions a Wohnungsanzeige, the meaning is clearly connected to housing.

Depending on the variety of English, you might translate it as:

• agent
• broker
• real-estate agent

Because German main clauses follow the verb-second rule.

In a normal statement, the finite verb must come in second position. Here the first position is occupied by Ich, so habe must come next:

Ich | habe | heute ...

That is why heute cannot go before habe in this version.

Compare:

• Ich habe heute eine Wohnungsanzeige gelesen.
• Heute habe ich eine Wohnungsanzeige gelesen.

Both are correct. The second one puts more emphasis on today.

But Ich heute habe ... is not the normal word order for a main clause.

Because sofort is modifying the action geschrieben, and this placement sounds natural and idiomatic.

The sentence highlights that the writing happened immediately:

... und sofort dem Makler geschrieben.

German adverb placement is somewhat flexible, so you may also hear:

... und dem Makler sofort geschrieben.

That is also possible, but the original version is very natural. Putting sofort early gives it a little more prominence.

Because all nouns are capitalized in German.

So in this sentence:

• Ich is capitalized because it is the first word of the sentence
• Wohnungsanzeige is capitalized because it is a noun
• Makler is capitalized because it is a noun

This is one of the most consistent spelling rules in German.

German often leaves that unstated if it is obvious from context.

Here, dem Makler geschrieben simply means wrote to the agent or contacted the agent in writing. The sentence does not specify whether it was an email, message, or letter.

If you want to be more explicit, you could say:

• Ich habe dem Makler sofort eine E-Mail geschrieben.
• Ich habe dem Makler sofort eine Nachricht geschrieben.

So the original sentence is completely natural; it just leaves the exact form of the message unspecified.