Moja kći se boji munje, ali se groma više ne boji toliko kao prije.

Because kći is a feminine singular noun in the nominative here, and the possessive adjective has to agree with it.

• moj = my
• moja = feminine singular nominative
• kći = daughter

So moja kći means my daughter.

Yes. The verb is bojati se, which means to be afraid or to fear.

It is normally learned as a fixed verb with se:

• bojim se = I am afraid
• boji se = he/she is afraid

So you should think of bojati se as the full dictionary form, not just bojati.

Because bojati se takes the genitive case.

So:

• munja → munje
• grom → groma

That is why Croatian says:

• bojati se munje
• bojati se groma

An English speaker often expects a direct object here, but Croatian uses genitive after this verb.

Here it means singular: of lightning.

The form munje can be ambiguous in isolation, because it can also appear in other grammatical uses, but in this sentence it is clearly singular genitive because it depends on boji se.

So:

• munja = lightning
• boji se munje = is afraid of lightning

They are related but not the same:

• munja = lightning
• grom = thunder, or sometimes thunderclap

So the sentence contrasts two different things:

• she is afraid of lightning
• she is no longer so afraid of thunder

Here više ne means no longer or not anymore.

Even though više often means more, when it combines with negation it very often means that something used to be true but is not true now.

So:

• više ne boji se / više se ne boji = she is no longer afraid
• više ne radi ovdje = he no longer works here

In this sentence:

• groma više ne boji = she is no longer afraid of thunder

Croatian word order is fairly flexible, and this sentence uses that flexibility for emphasis and natural rhythm.

A more neutral version would be something like:

• ali se više ne boji groma toliko kao prije
• or ali se groma više ne boji toliko kao prije

Both are understandable. In your sentence, groma is placed earlier to highlight the contrast with munje from the first clause.

So the effect is roughly:

• afraid of lightning, but of thunder she is no longer so afraid

Because se is a clitic, and Croatian clitics usually come near the beginning of a clause, often in the second position.

After ali, it is very natural to place se immediately after it:

• ali se ...

That is why you get:

• ali se groma više ne boji ...

This is normal Croatian clitic placement.

Because they belong to different parts of the sentence:

• se belongs to the verb bojati se
• ne negates the finite verb boji

In Croatian, ne normally goes directly before the finite verb:

• ne boji

So:

• se ... ne boji

This is completely normal.

It means as much as before or so much as before, depending on how you translate it.

Breakdown:

• toliko = so much / that much
• kao prije = as before / like before

Together:

• ne boji toliko kao prije = she is not as afraid as she used to be

This is a comparison between the present and the past.

Because Croatian often omits the subject when it is already clear from context.

The first clause gives the subject:

• Moja kći ...

Then the second clause keeps the same subject without repeating it:

• ali se groma više ne boji ...

The verb form boji is third person singular, and the listener naturally understands that it still refers to my daughter.

Yes. That is also a natural sentence.

It has a slightly more neutral word order:

• se više ne boji groma

The original version puts groma earlier for contrast:

• munje ... groma

So both are good, but the original sentence sounds a bit more stylistically shaped and contrastive.