Da meine Sprachpartnerin heute keine Zeit hat, schickt sie mir nur eine Sprachnachricht.

In this sentence, da means since / because, not there.

So:

• Da meine Sprachpartnerin heute keine Zeit hat, ... = Since/Because my language partner doesn’t have time today, ...

German da has more than one meaning:

• da = there in some contexts
• da = since / because in others

Here, because it introduces a whole clause with a verb at the end (hat), it is a subordinating conjunction meaning since/because.

Both da and weil can mean because.

In many cases, they are very similar:

• Da meine Sprachpartnerin heute keine Zeit hat, schickt sie mir nur eine Sprachnachricht.
• Weil meine Sprachpartnerin heute keine Zeit hat, schickt sie mir nur eine Sprachnachricht.

Both are correct.

A common difference in tone is:

• weil = the more neutral, everyday because
• da = often sounds a bit more formal, written, or like the reason is already known / obvious

Also, da-clauses are very often placed at the beginning of the sentence, as in your example.

Because the first clause is a subordinate clause introduced by da.

In German, subordinate clauses usually send the conjugated verb to the end.

So:

• da
  • subject + other elements + verb
• Da meine Sprachpartnerin heute keine Zeit hat

Compare:

• Main clause: Meine Sprachpartnerin hat heute keine Zeit.
• Subordinate clause: Da meine Sprachpartnerin heute keine Zeit hat

That final hat is one of the most important word-order patterns in German.

Because when a subordinate clause comes first, it takes up the first position in the sentence. In the following main clause, the verb must still be in second position.

Structure:

• [Da meine Sprachpartnerin heute keine Zeit hat], schickt sie mir nur eine Sprachnachricht.

The whole first clause counts as position 1. That means the conjugated verb of the main clause, schickt, must come next.

This is the same pattern as in sentences like:

• Heute geht er nach Hause.
• Wenn ich Zeit habe, gehe ich nach Hause.

So schickt sie is correct because German main clauses are verb-second (V2).

German usually uses kein to negate a noun that has no definite article.

Here, Zeit is a noun, and in this expression German says:

• Zeit haben = to have time
• keine Zeit haben = to not have time / to have no time

So:

• Sie hat keine Zeit. = She has no time / She doesn’t have time.

Use nicht for many other kinds of negation, but for an indefinite noun phrase like this, kein is the normal choice.

Compare:

• Ich habe ein Auto. → Ich habe kein Auto.
• Ich habe Zeit. → Ich habe keine Zeit.

Meine Sprachpartnerin means my female language partner / language exchange partner.

A few things are happening here:

• meine = my for a feminine noun in the nominative singular
• Sprachpartnerin is feminine

The base word is:

• der Sprachpartner = male language partner
• die Sprachpartnerin = female language partner

German often adds -in to make a feminine form for a person.

Because Sprachpartnerin is the subject of the clause, it is in the nominative, so the possessive is meine.

Mir is the dative form of ich.

The verb schicken often takes:

• a person receiving something in the dative
• the thing being sent in the accusative

So here:

• sie = subject
• mir = to me, indirect object, dative
• eine Sprachnachricht = a voice message, direct object, accusative

You can think of it as:

• She sends me a voice message.

Other examples:

• Sie gibt mir ein Buch.
• Er schreibt mir eine E-Mail.

Eine Sprachnachricht is the direct object of schickt, so it is in the accusative.

The noun Sprachnachricht is feminine:

• nominative: eine Sprachnachricht
• accusative: eine Sprachnachricht

For feminine nouns, the indefinite article is the same in nominative and accusative singular, so there is no visible change here.

That is why it stays:

• eine Sprachnachricht

Nur means only / just.

In this sentence:

• schickt sie mir nur eine Sprachnachricht

it means that the only thing she sends me is a voice message—for example, instead of having a longer conversation or call.

Its position before eine Sprachnachricht shows that it mainly modifies that noun phrase:

• only a voice message

So the idea is:

• She’s not doing more than that; she’s just sending a voice message.

They contain the same basic meaning, but they are used differently in the sentence.

• Meine Sprachpartnerin hat heute keine Zeit.
  This is a main clause: My language partner doesn’t have time today.

• Da meine Sprachpartnerin heute keine Zeit hat, ...
  This is a subordinate clause: Since my language partner doesn’t have time today, ...

So the second version connects that idea to another clause and gives the reason for what follows.

Yes. A very common alternative is to put the main clause first:

• Sie schickt mir heute nur eine Sprachnachricht, da meine Sprachpartnerin keine Zeit hat.

Or more naturally, keeping the same meaning:

• Sie schickt mir nur eine Sprachnachricht, da sie heute keine Zeit hat.

Both orders are possible. German often allows flexibility, but the word order rules inside each clause still apply:

• main clause: verb in second position
• subordinate clause with da: verb at the end

Because German uses a comma to separate a subordinate clause from a main clause.

Here:

• Da meine Sprachpartnerin heute keine Zeit hat, = subordinate clause
• schickt sie mir nur eine Sprachnachricht. = main clause

German punctuation is stricter than English in this area. When a subordinate clause is attached like this, the comma is normally required.

It is a compound noun:

• Sprache = language / speech
• Nachricht = message

In actual usage, Sprachnachricht means voice message.

German forms many nouns by combining smaller nouns into one long word, so this is a very typical German compound.