Musisz mieć cierpliwość, jeśli chcesz mówić po polsku coraz lepiej.

Polish often drops subject pronouns when the verb already makes the subject clear.

• musisz = you must / you have to
• chcesz = you want

Because those verb forms are clearly 2nd person singular, Polish does not need ty. You could say Ty musisz... or jeśli ty chcesz..., but that usually adds emphasis, contrast, or emotion.

So the version without ty is the most natural here.

Musisz is the 2nd person singular form of musieć (to have to / must) in the present tense.

A few forms of musieć:

• muszę = I must
• musisz = you must
• musi = he/she/it must
• musimy = we must
• musicie = you must (plural)
• muszą = they must

So Musisz mieć cierpliwość means You must have patience.

Mieć cierpliwość is a very common Polish expression meaning to have patience or to be patient.

Polish often uses mieć (to have) where English might sometimes prefer be:

• Mieć rację = to be right
• Mieć nadzieję = to hope
• Mieć czas = to have time
• Mieć cierpliwość = to have patience

So even though English might also say be patient, Polish naturally says have patience here.

Cierpliwość is in the accusative case, because it is the direct object of mieć.

• dictionary form: cierpliwość (nominative)
• direct object form: cierpliwość (accusative)

For many feminine nouns ending in -ość, the nominative and accusative look the same. So even though the case changes grammatically, the form does not change in spelling.

That is why you see:

• To jest cierpliwość (nominative, less common in real use)
• Musisz mieć cierpliwość (accusative)

In Polish, subordinate clauses are normally separated by a comma.

Here:

• Musisz mieć cierpliwość = main clause
• jeśli chcesz mówić po polsku coraz lepiej = subordinate clause

So the comma is required.

This is very normal in Polish:

• Zadzwoń, jeśli będziesz miał czas.
• Pójdę, jeśli nie będzie padać.

Because Polish often uses a conjugated verb plus an infinitive, just like English.

Here:

• chcesz = you want
• mówić = to speak

So chcesz mówić = you want to speak

This pattern is very common:

• Chcę iść = I want to go
• Muszę pracować = I have to work
• Lubię czytać = I like to read

Only the first verb is conjugated; the second stays in the infinitive.

Mówić is the right choice because the sentence is about the general ability or process of speaking Polish better over time.

• mówić = to speak, to be speaking, to talk
• powiedzieć = to say something / to tell / to state, usually as a completed act

Here the idea is not say one thing once, but speak the language more and more well, so mówić fits.

Also, mówić is imperfective, which suits ongoing, repeated, developing action.

When talking about the language used, Polish commonly says po + adjective in the locative form.

So:

• po polsku = in Polish
• po angielsku = in English
• po niemiecku = in German
• po hiszpańsku = in Spanish

This is a standard pattern. Even though English uses in, Polish usually uses po in this expression.

Because after po in this kind of language expression, Polish uses a special fixed form based on the locative.

So:

• polski = Polish (basic adjective form)
• po polsku = in Polish

You do not say po polski here.

Compare:

• polski język = the Polish language
• mówić po polsku = to speak in Polish

This is something learners usually just memorize as a pattern: po + language form

Coraz lepiej means better and better or increasingly well.

It has two parts:

• coraz = more and more / increasingly
• lepiej = better (comparative adverb of dobrze = well)

So:

• dobrze = well
• lepiej = better
• coraz lepiej = better and better

This is a very common pattern:

• coraz więcej = more and more
• coraz szybciej = faster and faster
• coraz trudniej = more and more difficultly / increasingly difficult

Because the sentence needs an adverb, not an adjective.

• lepszy = better (adjective, used with nouns)
• lepiej = better (adverb, used with verbs)

Here lepiej describes mówić (to speak), so it must be an adverb:

• mówić lepiej = to speak better

Compare:

• To jest lepsza książka. = This is a better book.
  (lepsza describes książka)
• Mówię lepiej po polsku. = I speak Polish better.
  (lepiej describes mówię)

Not with the same meaning.

• jeśli chcesz mówić po polsku coraz lepiej = if you want to speak Polish better and better
• żeby mówić po polsku coraz lepiej = in order to speak Polish better and better

So jeśli introduces a condition:

• if you want X, you must do Y

But żeby introduces a purpose:

• to achieve X, you must do Y

Both are possible in different sentences, but they do not mean the same thing.

Not completely. Polish word order is fairly flexible, but the given version is natural and neutral.

Standard sentence:

• Musisz mieć cierpliwość, jeśli chcesz mówić po polsku coraz lepiej.

You could move things around for emphasis, for example:

• Jeśli chcesz mówić po polsku coraz lepiej, musisz mieć cierpliwość.

That version is also very natural and puts the if-clause first.

But some changes would sound unusual or overly marked unless you had a special reason. So learners should treat the original sentence as a good default model.

Yes, Musisz być cierpliwy means You must be patient, and it is very natural Polish.

The difference is mainly stylistic:

• Musisz mieć cierpliwość = You must have patience
• Musisz być cierpliwy = You must be patient

Both are correct. The sentence you were given uses the noun cierpliwość, while the alternative uses the adjective cierpliwy.

So this is not a grammar mistake issue; it is just a different but equally natural way to express a similar idea.