Wir stiegen später noch einmal um, weil auf dem anderen Bahnsteig eine technische Panne auftrat.

In a travel context, umsteigen means to change trains / transfer.

So Wir stiegen ... um means we changed or we transferred. German often leaves out the vehicle if it is obvious from context, so you do not need to say exactly from one train to another every time.

Because umsteigen is a separable verb.

Its basic form is umsteigen, but in a normal main clause, the prefix um- splits off and goes to the end:

• Wir steigen um.
• Wir stiegen um.

So in your sentence:

• stiegen = the conjugated verb part
• um = the separated prefix

This is a very common pattern in German.

Stiegen is the simple past form of steigen.

The full verb is umsteigen, but the core strong verb is steigen, whose past forms are:

• infinitive: steigen
• simple past: stieg
• plural simple past: stiegen
• past participle: gestiegen

Because the subject is wir, the form is stiegen.

So:

• ich stieg um
• wir stiegen um

Both are possible, but they belong to different styles.

• Wir stiegen später noch einmal um = simple past, common in written narration
• Wir sind später noch einmal umgestiegen = perfect tense, more common in everyday spoken German

A native speaker would very likely say the perfect tense in conversation, but the simple past is completely normal in writing.

Also note that umsteigen forms the perfect with sein, not haben:

• Wir sind umgestiegen.

It means something like later on, one more time or later, again.

The two parts add slightly different ideas:

• später = later
• noch einmal = once again / one more time

So the sentence suggests that they had to change trains again at a later point.

A useful nuance:

• noch einmal often stresses an additional occurrence
• wieder can also mean again, but is a bit broader

Here noch einmal fits well because it emphasizes one more transfer.

Because weil introduces a subordinate clause, and in German subordinate clauses the conjugated verb goes to the end.

So:

• main clause: Wir stiegen später noch einmal um
• subordinate clause: weil ... eine technische Panne auftrat

This is one of the most important German word-order rules.

Compare:

• Eine technische Panne trat auf.
  main clause

• ..., weil eine technische Panne auftrat.
  subordinate clause

Because auftreten is also a separable verb, but separable verbs behave differently depending on clause type.

In a main clause, the prefix separates:

• Eine Panne trat auf.

In a subordinate clause, the verb goes to the end and the prefix stays attached:

• ..., weil eine Panne auftrat.

So:

• umsteigen → stiegen ... um in the main clause
• auftreten → auftrat at the end of the subordinate clause

That contrast is very typical in German.

Because auf can take either dative or accusative, depending on meaning:

• dative = location, where?
• accusative = direction/movement, where to?

Here the sentence means the technical problem occurred on the other platform, so this is a location idea:

• auf dem anderen Bahnsteig = on the other platform

If it meant movement toward the platform, you would expect accusative:

• auf den anderen Bahnsteig

But that is not the meaning here.

Because it is an adjective-like word following dem, which is dative masculine.

The noun is:

• der Bahnsteig (masculine)

In the dative singular with the definite article:

• dem Bahnsteig

And the adjective or determiner-like word before it takes the ending -en:

• dem anderen Bahnsteig

So anderen is there because of the case/gender pattern, not because of anything special about the meaning.

This is a very useful vocabulary distinction.

• Bahnsteig = platform
  the place where passengers stand and board the train

• Gleis = track / rail line
  the rails the train runs on

So auf dem anderen Bahnsteig means on the other platform, not on the other track.

English speakers often mix these up, because station vocabulary does not match one-to-one across languages.

Yes, technische Panne is a natural phrase. It means a technical problem, technical malfunction, or breakdown.

The verb auftreten here means to occur, to arise, or to happen.

So:

• eine technische Panne auftrat = a technical problem occurred

Also, Panne is not only for car trouble. It can also be used for machines, systems, equipment, or transport problems, so it works well in this sentence.