Ich schalte die SIM-Karte frei.

Because the verb here is the separable verb freischalten.

In a normal main clause, German splits many separable verbs:

• the conjugated part goes to position 2
• the prefix goes to the end

So:

• freischalten → Ich schalte ... frei.

That is why you do not say Ich freischalte die SIM-Karte in a normal main clause.

Compare:

• Ich schalte die SIM-Karte frei.
• Wir schalten die SIM-Karte frei.

This is one of the most important German word-order patterns to learn.

The infinitive is freischalten.

In the present tense, it goes like this:

• ich schalte frei
• du schaltest frei
• er/sie/es schaltet frei
• wir schalten frei
• ihr schaltet frei
• sie/Sie schalten frei

So in your sentence, schalte is the ich form.

Because Karte is a feminine noun in German, so its article is die.

The important part is the main noun Karte, not SIM.
SIM just specifies what kind of card it is.

So:

• die Karte
• die SIM-Karte

The hyphen is normal in German when an abbreviation like SIM is combined with a noun.

It is in the accusative case, because it is the direct object of the verb.

The sentence answers the question:

• What am I unlocking/activating?
• die SIM-Karte

So:

• Ich = subject, nominative
• die SIM-Karte = direct object, accusative

A small detail: for feminine nouns, nominative die and accusative die look the same, so the article does not change here.

Not exactly. Here, frei is part of the separable verb freischalten.

So in this sentence, it is better to think of schalte ... frei as one complete verbal idea, not as:

• schalten = switch
• frei = free

German often forms verbs this way:

• aufmachen → Ich mache die Tür auf.
• anmachen → Ich mache das Licht an.
• freischalten → Ich schalte die SIM-Karte frei.

So frei keeps its literal sense of free/open/unblocked, but in this sentence it functions as part of the verb.

Yes. You keep it together when it is not being used as a finite verb in a main clause.

For example:

• Ich möchte die SIM-Karte freischalten.
  Here it is an infinitive, so it stays together.

• ..., weil ich die SIM-Karte freischalte.
  In a subordinate clause, the conjugated verb goes to the end, and the separable verb is written together.

So:

• main clause: Ich schalte die SIM-Karte frei.
• infinitive: die SIM-Karte freischalten
• subordinate clause: weil ich die SIM-Karte freischalte

Sometimes yes, but the nuance can be a little different.

• freischalten often means activate, enable, or unlock for use
• entsperren often means unlock in the sense of removing a lock or block

In technical and phone-related contexts, freischalten is very common for things like:

• activating a SIM card
• enabling a feature
• unlocking access

entsperren is also common, especially for:

• unlocking a phone
• unlocking a screen
• unblocking something after it was locked

So for a SIM card, freischalten sounds very natural.

German nouns are capitalized, so Karte must have a capital K.

The hyphen is used because SIM is an abbreviation attached to a noun. This is very common in German.

Examples:

• SIM-Karte
• E-Mail-Adresse
• USB-Kabel

So the spelling in your sentence is completely standard:

• die SIM-Karte

A very common past form would be the Perfekt:

• Ich habe die SIM-Karte freigeschaltet.

Here:

• habe is the auxiliary verb
• freigeschaltet is the past participle of freischalten

Notice that the participle is written as one word:

• freischalten → freigeschaltet

So the pattern is:

• present: Ich schalte die SIM-Karte frei.
• perfect: Ich habe die SIM-Karte freigeschaltet.