Odwaga pomaga mi mówić po polsku.

Odwaga means courage and it is the subject of the sentence — the thing doing the helping.

It is in the nominative case, which is the normal case for the subject of a sentence in Polish. So:

• odwaga = courage
• pomaga = helps
• mi = me / to me
• mówić po polsku = to speak Polish

So grammatically, odwaga is the noun that matches the verb pomaga.

Also, odwaga is a feminine noun, which is why in the past tense you would see feminine agreement, for example odwaga pomogła mi....

Because the verb pomagać / pomóc normally takes the dative case for the person receiving help.

So:

• mi = dative form of ja in its short/clitic version
• mnie = can be accusative or dative, but it is the full/stressed form

With pomagać, the normal pattern is:

• pomagać komuś = to help someone

Examples:

• Pomaga mi. = He/she/it helps me.
• Pomaga ci. = He/she/it helps you.
• Pomaga mu. = He/she/it helps him.

So mnie would not be wrong in every situation, but mi is the usual neutral form here.

Both can mean me, but they are used differently.

mi

This is the unstressed, shorter form. It is very common in ordinary sentences.

• Odwaga pomaga mi mówić po polsku.

mnie

This is the full/stressed form. It is used:

• for emphasis
• after some prepositions
• when you want contrast

Examples:

• Odwaga pomaga mnie, nie tobie. = Courage helps me, not you.
  (This sounds contrastive/emphatic.)
• Dla mnie = for me

So in your sentence, mi sounds the most natural because there is no special emphasis.

Because after pomagać in this kind of structure, Polish commonly uses the infinitive.

The pattern is:

• pomagać komuś + infinitive
• help someone do something

So:

• pomaga mi mówić = helps me speak

Compare:

• Pomaga mi pracować. = It helps me work.
• Pomaga mi zrozumieć. = It helps me understand.

If you said mówię, that would be a finite verb meaning I speak, and it would not fit this structure.

Because Polish has a special common pattern for languages:

• mówić po + adjective-like form

So:

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

This is the standard way to say to speak in a language.

Why not polski?

Polski is the basic adjective form meaning Polish, but after po in this expression, Polish uses a different form.

Why not w polskim?

W polskim usually means in Polish in a different sense, for example:

• w polskim domu = in a Polish house
• w polskim tekście = in a Polish text

For languages with speak, the normal phrase is mówić po polsku.

Historically and grammatically, this form is treated as the locative after po in this expression.

That is why you get:

• po polsku
• po angielsku
• po francusku

For a learner, the most practical thing is to memorize this as a fixed pattern:

• mówić po + language form

You do not need to build it from scratch every time at the beginning. Just learn:

• po polsku
• po angielsku
• po hiszpańsku, etc.

Yes, pomaga is 3rd person singular present tense of pomagać.

Because Polish present tense often covers both:

• a general truth / habitual meaning
• an action happening now

this sentence can mean something like:

• Courage helps me speak Polish
• Courage is helping me speak Polish

In many contexts, the more natural English translation is the general one: Courage helps me speak Polish.

Also, pomagać is imperfective, which fits an ongoing, repeated, or general idea.

Yes, the word order can change, because Polish is more flexible than English thanks to its case system.

The neutral, natural order here is:

• Odwaga pomaga mi mówić po polsku.

But other orders are possible for emphasis, for example:

• Mi odwaga pomaga mówić po polsku.
• Po polsku odwaga pomaga mi mówić.

These alternatives are not the most neutral everyday wording, but they can appear if the speaker wants to emphasize a particular part.

For learners, it is best to keep the standard order:

• subject + verb + indirect object + infinitive phrase

Because Polish has no articles.

English distinguishes:

• courage
• the courage
• a courage (though this last one is unusual in English)

Polish simply uses the noun:

• odwaga

Whether it means courage, the courage, or something more context-specific depends on the situation.

That is normal in Polish:

• Kobieta mówi. = The woman is speaking / A woman is speaking
• Odwaga pomaga. = Courage helps / The courage helps

Context tells you which meaning is intended.