Potrubí je poškozené, což je problém.

Usually potrubí means pipework, piping, or a pipeline/system of pipes, not just one individual pipe.

If you want to talk about a single pipe, Czech more often uses trubka.

So:

• potrubí = pipework / piping / pipeline
• trubka = a pipe / tube

In this sentence, potrubí is a neuter noun and it is treated as singular: Potrubí je poškozené = The pipework is damaged.

Because it agrees with potrubí.

In Czech, adjectives and adjective-like forms must agree with the noun in gender, number, and case.
Potrubí is neuter singular, so the form is poškozené.

Compare:

• masculine: poškozený
• feminine: poškozená
• neuter: poškozené

So:

• poškozený kabel = damaged cable
• poškozená trubka = damaged pipe
• poškozené potrubí = damaged pipework

Even though the adjective comes after je, it still agrees with potrubí.

It is very commonly used like an adjective, but technically it comes from a past passive participle of the verb poškodit = to damage.

So literally it means something like damaged or having been damaged.

In normal usage, though, you can safely think of poškozený / poškozená / poškozené as an adjective meaning damaged.

Because there are really two linked statements:

1. Potrubí je poškozené = The pipework is damaged.
2. což je problém = which is a problem.

So each part needs its own je:

• first je connects potrubí with poškozené
• second je connects což with problém

Both are just the present tense of být = to be.

Here což means which, but not in the simple noun-referring way English learners often expect.

It refers to the whole previous idea, not just to potrubí by itself.

So:

• Potrubí je poškozené, což je problém.
• The pipework is damaged, which is a problem.

Here což = the fact that the pipework is damaged.

That is one of the most important uses of což in Czech.

Because což refers to the whole previous clause, while který / která / které usually refers to a specific noun.

Compare:

• Potrubí je poškozené, což je problém.
  = The pipework is damaged, which is a problem.
  Here což refers to the whole fact.

• Potrubí, které je poškozené, je staré.
  = The pipework that is damaged is old.
  Here které refers directly to potrubí.

So in your sentence, což is the natural choice.

It refers to the whole statement Potrubí je poškozené.

So the meaning is not:

• the pipework, which is a problem

but rather:

• the fact that the pipework is damaged is a problem

That is why což works so well here.

Because což introduces a subordinate clause, and Czech normally separates that with a comma.

So:

• Potrubí je poškozené, což je problém.

This is standard Czech punctuation.

It is similar to English in sentences like:

• The pipework is damaged, which is a problem.

The comma is not optional here in normal written Czech.

It is in the nominative singular.

In this sentence, problém is the predicate noun after je:

• což je problém = that is a problem

So problém is not in the accusative here. It is naming what což is.

A useful parallel is:

• To je problém. = That is a problem.
• To je chyba. = That is a mistake.

Yes, absolutely.

That version is perfectly understandable and natural:

• Potrubí je poškozené. To je problém.

Compared with což je problém, it sounds a bit more direct and split into two separate statements.

Very roughly:

• což je problém = slightly smoother, more connected, often a bit more written/formal
• To je problém. = simpler, more straightforward

Both are good.

Yes, Czech word order is flexible, but the original order is the most neutral and natural here:

• Potrubí je poškozené, což je problém.

If you change the order, the emphasis changes.

For example:

• Poškozené je potrubí.
  Grammatically possible, but marked; it sounds like you are emphasizing damaged or contrasting it with something else.

• Problém je, že potrubí je poškozené.
  Also natural, but now the sentence is organized around the problem is that...

So the original sentence is probably the best basic model for learners.

Usually closer to damaged.

Poškozený / poškozená / poškozené is a broad word. It can describe something that is cracked, harmed, impaired, or otherwise not in proper condition.

If you specifically mean broken, Czech might use something like rozbitý in some contexts. But for infrastructure, equipment, or pipework, poškozené is often the better and more natural choice.

So:

• poškozené potrubí = damaged pipework
• rozbitá trubka might sound more like a physically broken pipe

In your sentence, poškozené is a very natural choice.