Mamy jeszcze piętnaście minut do końca lekcji.

Yes. Mamy is the 1st person plural form of mieć (to have), so literally it means we have.

In Polish, mieć is often used in expressions about time available / time left, so:

• Mamy jeszcze piętnaście minut. = We still have fifteen minutes.
• very naturally in English: There are still fifteen minutes left / We’ve still got fifteen minutes left

So this is a normal Polish way to talk about remaining time.

Because Polish usually does not need subject pronouns unless you want emphasis or contrast.

The ending of the verb already shows the subject:

• mam = I have
• masz = you have
• mamy = we have

So Mamy already means we have.
You could say My mamy..., but that would sound emphatic, like we have... as opposed to someone else.

Here jeszcze means still.

So:

• Mamy piętnaście minut. = We have fifteen minutes.
• Mamy jeszcze piętnaście minut. = We still have fifteen minutes.

Depending on context, jeszcze can also mean more / another, but in this sentence the meaning is clearly still.

Because after numbers like 5 and above, Polish normally uses the noun in the genitive plural form.

So:

• 1 minuta
• 2, 3, 4 minuty
• 5+ minut

Examples:

• jedna minuta
• dwie minuty
• cztery minuty
• pięć minut
• piętnaście minut

So piętnaście minut is the correct form.

The form minut is the genitive plural of minuta.

That happens because of the numeral piętnaście. In Polish, numbers 5 and higher usually require the counted noun to appear in the genitive plural:

• pięć minut
• dziesięć minut
• piętnaście minut

So even though the whole phrase functions as the object of mamy, the noun itself appears in the form minut.

Do is a preposition that usually takes the genitive case and often means to, until, or up to.

Here:

• do końca = until the end / to the end
• lekcji = of the lesson

So:

• koniec = end
• końca = genitive form of koniec
• lekcja = lesson
• lekcji = genitive form of lekcja

Together, do końca lekcji means until the end of the lesson.

Because both are in the genitive.

1. do requires the genitive:

   • do końca

2. Then koniec is followed by of what?

   • koniec lekcji = the end of the lesson

So:

• koniec → końca
• lekcja → lekcji

This is very common in Polish:

• do domu = to home
• do szkoły = to school
• do końca dnia = until the end of the day

Yes. Polish word order is quite flexible.

The original sentence:

• Mamy jeszcze piętnaście minut do końca lekcji.

Possible alternatives:

• Do końca lekcji mamy jeszcze piętnaście minut.
• Jeszcze mamy piętnaście minut do końca lekcji.

The original version sounds very natural and neutral.
Changing the order usually changes emphasis, not the basic meaning.

For example:

• Do końca lekcji at the front emphasizes until the end of the lesson
• jeszcze placed earlier can emphasize the idea of still

It can often correspond to English lesson or class, depending on context.

• lekcja often means a school lesson, a class period, or one lesson in a course.
• In this sentence, English could naturally say either:
  • until the end of the lesson
  • until class ends

So the Polish word is tied to the idea of a lesson/class period.

Yes, it is natural and correct.

A few other natural Polish ways are:

• Zostało jeszcze piętnaście minut do końca lekcji.
• Mamy jeszcze piętnaście minut do końca lekcji.

The version with mamy feels a bit like we still have fifteen minutes left, while zostało is closer to there are fifteen minutes left.

Both are common.

A rough pronunciation guide:

• piętnaście ≈ pyen-NAHSH-cheh
• lekcji ≈ LEK-tsyee

A few helpful notes:

• ę in pię- is a nasal vowel, but in normal speech before certain consonants it may sound closer to pyen
• ś sounds like a soft sh
• cj in lekcji gives a tsy-type sound

If you are a beginner, a reasonable first approximation is:

• Mamy jeszcze piętnaście minut do końca lekcji
• ≈ MAH-my YESH-che PYEN-NAHSH-che MEE-noot do KOHN-tsa LEK-tsyee

Yes, absolutely in normal writing such as messages, notes, or informal materials:

• Mamy jeszcze 15 minut do końca lekcji.

That is completely normal.
In textbooks or more formal prose, numbers may be written out as words:

• piętnaście

Both represent the same sentence.