Venku je bouřka, ale moje dcera se jí nebojí.

Venku is an adverb meaning outside / outdoors.

Czech often uses it by itself, without anything like na or v. So:

• Venku je bouřka. = There’s a storm outside.
• literally, something like Outside is a storm.

It works as a scene-setting adverb at the start of the sentence.

Czech often uses je + noun to describe weather or a situation:

• Je zima. = It’s cold.
• Je mlha. = It’s foggy / There is fog.
• Je bouřka. = There’s a storm / It’s stormy.

So bouřka is the subject here, in the nominative singular.

Also, Czech has no articles, so there is no word for a in a storm.

Not exactly.

• bouřka usually means thunderstorm
• bouře is a broader word meaning storm

In everyday Czech, bouřka is the natural choice when you mean the kind of storm with thunder and lightning.

Both are possible.

• moje dcera
• má dcera

Both mean my daughter.

For many learners, the simplest takeaway is:

• moje dcera is very common and natural in everyday speech
• má dcera is also correct, but can sound a bit more formal, literary, or stylistically tighter

So in this sentence, moje dcera is completely normal.

Because the Czech verb is bát se = to be afraid.

Here, se is just part of the verb. It does not literally mean herself.

This is very common in Czech: some verbs are reflexive in form, even when English uses a non-reflexive verb.

So:

• bát se = to be afraid
• moje dcera se bojí = my daughter is afraid
• moje dcera se nebojí = my daughter is not afraid

Jí refers back to bouřka.

So the second clause literally means:

• my daughter is not afraid of it
• where it = the storm

Czech often uses a pronoun like this instead of repeating the noun.

Because bát se takes the genitive case:

• bát se koho / čeho = to be afraid of someone / something

The pronoun referring to bouřka must therefore be in the genitive:

• jí = of her / of it here

If you used ji, that would be the accusative, which is not what bát se requires.

So:

• bojí se jí = correct
• bojí se ji = incorrect

Yes, absolutely.

That version repeats the noun instead of using a pronoun:

• moje dcera se bouřky nebojí = my daughter isn’t afraid of the storm

Here bouřky is the genitive singular of bouřka, because again bát se requires the genitive.

So both are natural:

• moje dcera se jí nebojí
• moje dcera se bouřky nebojí

The version with jí simply avoids repetition.

This is because se and jí are both unstressed clitics. In neutral Czech word order, clitics usually go early in the clause, typically after the first stressed element.

In this clause:

• ale | moje dcera | se jí | nebojí

After ale, the first real clause element is moje dcera, so the clitics se jí come right after it.

That makes moje dcera se jí nebojí the most natural neutral order.

You can also have nebojí se jí when the verb comes first, for example as a shorter sentence on its own:

• Nebojí se jí. = She isn’t afraid of it.

So the verb and se still belong together grammatically, but Czech word order moves clitics around.

It is the 3rd person singular present of bát se, with negation:

• bojí se = he/she is afraid
• nebojí se = he/she is not afraid

Czech usually makes verbal negation by adding ne- directly to the verb:

• je → není
• má → nemá
• bojí se → nebojí se

In your sentence, because of clitic placement, you see:

• se jí nebojí

but the verb form itself is still nebojí.

It is nominative singular, because it is the subject of the second clause.

• dcera = nominative singular
• moje agrees with it in gender, number, and case

So moje dcera is the person doing the action of not being afraid.

Because ale means but, and here it joins two clauses:

• Venku je bouřka
• ale moje dcera se jí nebojí

In Czech, a comma is normally written before ale in this kind of sentence. That is very standard punctuation.