Kłopot zaczyna się po terminie zwrotu.

Kłopot is singular and means trouble, a problem, or a hassle.

In this sentence, the singular is used in a fairly general way, like English the trouble starts... or the problem begins... It does not have to mean exactly one specific problem.

You could also say Kłopoty zaczynają się po terminie zwrotu, which would mean Problems start after the return deadline or Trouble starts after the return deadline in a more plural sense.

Because the verb here is zaczynać się / zacząć się, which means to begin or to start.

• zaczynać coś = to start something
• zaczynać się = to begin / to start

So:

• Zaczynam pracę. = I start work.
• Praca zaczyna się o ósmej. = Work begins at eight.

In your sentence, kłopot is the thing that begins, so Polish uses zaczyna się.

It is in the locative singular.

The preposition po often requires the locative when it means after in a time sense.

So:

• po terminie = after the deadline / after the due date

The base form is termin, and the locative singular is terminie.

In time expressions, po commonly means after.

Examples:

• po obiedzie = after lunch
• po pracy = after work
• po terminie = after the deadline

So po terminie zwrotu means after the return deadline or after the due date for returning it.

Because zwrotu is the genitive singular form of zwrot.

Here, termin zwrotu means literally deadline/date of return. In Polish, nouns like termin often take another noun in the genitive to show what the deadline is for.

Compare:

• termin płatności = payment deadline
• termin oddania = return/submission deadline
• termin zwrotu = return deadline

So the pattern is:

• termin + genitive

That is why it is zwrotu.

Here termin means deadline, due date, or set date.

It does not mean the English word term in the sense of a school semester or technical vocabulary term.

So termin zwrotu is best understood as:

• return deadline
• due date for return
• date by which something must be returned

Zwrot can mean different kinds of return, depending on context.

Common meanings include:

• returning an item
• a refund
• a turn/phrase in some contexts

In termin zwrotu, the most natural meaning is the deadline for returning something, especially in contexts like books, rentals, borrowed items, library materials, or purchases.

If the broader context were about money, it might possibly suggest refund, but in this sentence return deadline is the most likely reading.

No, Polish word order is fairly flexible.

The sentence Kłopot zaczyna się po terminie zwrotu is a natural, neutral order.

But other orders are possible, for example:

• Po terminie zwrotu kłopot się zaczyna.
• Po terminie zwrotu zaczyna się kłopot.

These can sound slightly different in emphasis, but the core meaning stays the same.

The original version sounds straightforward and natural.

Yes, you could say:

• Problem zaczyna się po terminie zwrotu.

That is also natural.

The difference is slight:

• kłopot often feels like trouble, difficulty, or hassle
• problem feels more like problem in the direct English sense

In many contexts, either word would work.

A rough pronunciation guide is:

Kłopot zaczyna się po terminie zwrotu
KWO-pot za-CHY-na shye po ter-MEE-nye ZVRO-tu

A few helpful points:

• ł sounds like English w
• cz sounds like ch in chocolate
• się sounds roughly like shye, with a nasalized vowel at the end in careful speech
• rz / ż usually sound like the s in measure, but in zwrotu the cluster is pronounced with a voiced retroflex sound after v

You do not need perfect phonetics at first; saying it approximately as
KWO-pot za-CHY-na shye po ter-MEE-nye ZVRO-tu
will already be quite understandable.