Jeg har tænkt mig at blive hjemme i aften, medmindre min søster ringer og siger, at forestillingen stadig har ledige pladser.

It is an idiomatic way to say intend to or am planning to.

So:

Jeg har tænkt mig at blive hjemme = I intend to stay home

The reflexive pronoun is part of the expression, and it changes with the subject:

• jeg har tænkt mig
• du har tænkt dig
• han/hun har tænkt sig
• vi har tænkt os

So you learn it as a set phrase: at have tænkt sig at + infinitive.

Yes, blive often means become, but in the expression blive hjemme, it means stay home or remain at home.

So:

• være hjemme = be at home
• blive hjemme = stay home

Here the speaker is talking about a decision not to go out, so blive hjemme is the natural choice.

I aften means tonight or this evening, depending on context.

• aften = evening
• i aften = tonight / this evening

A useful contrast:

• i aften = tonight in the evening
• i nat = tonight during the night

Medmindre means unless.

It introduces the condition that would change the speaker’s plan:

• Jeg har tænkt mig at blive hjemme i aften, medmindre ...
• I’m planning to stay home tonight, unless ...

So the basic structure is:

X, medmindre Y = X, unless Y

Because Danish often uses the present tense to talk about future events when the future meaning is clear from context.

Here, it is obviously about a possible future situation:

• medmindre min søster ringer
• unless my sister calls

This is very common in Danish, especially after words like:

• hvis = if
• når = when
• medmindre = unless

So present tense here does not mean it is happening right now.

Here at means that and introduces a subordinate clause:

• siger, at forestillingen stadig har ledige pladser
• says that the performance still has available seats

This is very common after verbs like:

• sige = say
• tro = think/believe
• vide = know
• håbe = hope

In informal spoken Danish, at is sometimes omitted, but keeping it is clear and standard.

Because this part of the sentence is a subordinate clause introduced by at.

In Danish, sentence adverbs such as stadig, ikke, ofte, and altid usually come before the finite verb in subordinate clauses.

Compare:

• Main clause: Forestillingen har stadig ledige pladser.
• Subordinate clause: ... at forestillingen stadig har ledige pladser.

So the word order changes because of the subordinate clause.

Forestillingen means the performance, the show, or the presentation, depending on context.

It is definite because it refers to a specific performance that the speaker and listener already know about.

Compare:

• en forestilling = a performance / a show
• forestillingen = the performance / the show

So Danish uses the definite form here for the same reason English uses the.

Literally, it means free/vacant places, but in this context the natural English meaning is available seats or seats left.

• ledig = free, vacant, available
• plads = place, seat, space
• ledige pladser = available seats / spaces available

With a show, cinema, train, or restaurant, ledige pladser usually means there is still room.

This sentence is written with start commas, which are a traditional and accepted Danish comma style.

That is why you see commas before subordinate clauses:

• before medmindre
• before at forestillingen ...

You may also see modern Danish written without these start commas:

Jeg har tænkt mig at blive hjemme i aften medmindre min søster ringer og siger at forestillingen stadig har ledige pladser.

So if you notice different comma usage in Danish, that is normal. Both systems are accepted if used consistently.