Na kursie polskiego trzeba mieć cierpliwość.

In Polish, na is often used for activities, events, classes, and courses.

So:

• na kursie = at/on a course
• na lekcji = in class / during the lesson
• na spotkaniu = at the meeting

By contrast, w is more often used for being physically inside a place or within something.

Also, after na in the meaning of location, Polish uses the locative case, which is why kurs becomes kursie.

Because na here expresses location, and that requires the locative case.

The noun changes like this:

• kurs = course
• na kursie = at/on the course

This is a normal masculine noun pattern:

• dom → w domu
• uniwersytet → na uniwersytecie
• kurs → na kursie

So kursie is simply the locative singular form of kurs.

Because polskiego is in the genitive case.

In kurs polskiego, the structure is basically:

• kurs czego? = a course of what?
• polskiego = of Polish

So kurs polskiego means a Polish course or more literally a course of Polish.

This is very common in Polish:

• nauczyciel angielskiego = English teacher
• lekcja historii = history lesson
• kurs polskiego = Polish course

Grammatically, it is the form of the adjective polski (Polish), but here it functions as part of an implied phrase.

The full idea is often understood as:

• kurs języka polskiego = a course of the Polish language

Very often, języka is omitted because the meaning is obvious, so you just get:

• kurs polskiego

So learners often see polskiego and wonder, Polish what? The answer is: it really means Polish language, with języka left out.

Trzeba means something like:

• it is necessary
• one must
• you have to
• it takes (in some contexts)

In this sentence, it expresses a general necessity, not something tied to a specific person.

So:

• trzeba mieć cierpliwość = you need to have patience / one needs to have patience

A key point: trzeba is impersonal. It does not change for person:

• not trzebam
• not trzebasz
• not trzebałem

It always stays trzeba.

Because after trzeba, Polish normally uses an infinitive.

So the pattern is:

• trzeba + infinitive

Examples:

• trzeba pracować = you have to work
• trzeba czekać = you have to wait
• trzeba mieć cierpliwość = you need to have patience

This is similar to English have to + verb or need to + verb, except Polish uses the impersonal word trzeba plus the infinitive.

Because cierpliwość is the direct object of mieć.

• mieć co? = to have what?
• cierpliwość = patience

That means it should be in the accusative case. The important detail is that for this noun, the nominative and accusative singular look the same:

• nominative: cierpliwość
• accusative: cierpliwość

So the form does not visibly change, even though the grammatical role does.

Yes, you can.

• trzeba mieć cierpliwość = you need to have patience
• trzeba cierpliwości = patience is needed / you need patience

The second version is a bit more compact and uses the genitive:

• cierpliwość → cierpliwości

Both are natural.
The version with mieć sounds slightly more like to possess/show patience, while trzeba cierpliwości is a more direct statement that patience is necessary.

No explicit subject is stated.

That is because trzeba creates an impersonal sentence. Polish often does this when talking about general rules, obligations, or necessities.

So instead of saying:

• you need patience
• people need patience
• one needs patience

Polish simply says:

• trzeba mieć cierpliwość

The subject is understood in a general sense.

Yes. Polish word order is fairly flexible, although the neutral version here is:

• Na kursie polskiego trzeba mieć cierpliwość.

Other orders are possible, for example:

• Trzeba mieć cierpliwość na kursie polskiego.
• Cierpliwość trzeba mieć na kursie polskiego.

These versions shift the emphasis a bit:

• starting with Na kursie polskiego emphasizes the setting
• starting with Trzeba emphasizes the necessity
• starting with Cierpliwość emphasizes the thing required

The original sentence sounds very natural and neutral.

Literally, yes, Polish uses na, which often translates word-for-word as on. But in natural English, you would usually say:

• in a Polish class
• at a Polish course
• on a Polish course (also possible, especially in British English)

So it is best not to translate na mechanically every time. In Polish, na is just the normal preposition used with many organized activities like courses, lessons, workshops, and meetings.

It would be similar, but not exactly the same.

• na kursie polskiego = at/in the Polish course, during participation in it
• podczas kursu polskiego = during the Polish course

Podczas focuses more specifically on the time period, while na kursie is the more everyday way to say in class / on the course / while attending the course.

So in this sentence, na kursie polskiego is the most natural choice.

Usually it sounds general, especially because there is no word like tym (this) or tym kursie (that course / this course).

So the sentence is understood as something like:

• In a Polish course, you need patience
• When learning Polish in a course, patience is necessary

If you wanted to make it specific, you could say:

• Na tym kursie polskiego trzeba mieć cierpliwość.
  = On this Polish course, you need patience.

That makes it sound more like a comment about one particular course.