Moja kći kaže da je žirafa smiješna, a zebra ljepša od svih drugih životinja.

Because moja has to agree with kći in gender, number, and case.

• kći = daughter
• It is a feminine singular noun here
• So the possessive adjective must also be feminine singular: moja

Compare:

• moj sin = my son
• moja kći = my daughter
• moje dijete = my child

Yes. Kći is a fairly irregular and slightly old-looking noun form for English speakers, both in spelling and declension. It is a very common word, though, so it is worth memorizing as a special item.

In this sentence, kći is in the nominative singular because it is the subject of kaže.

It means says that is, or more naturally in English, says that ... is ...

• kaže = says
• da = that
• je = is

So:

• Moja kći kaže da je žirafa smiješna
  = My daughter says that the giraffe is funny

Because je is a clitic. In Croatian, clitics usually go in the second position in their clause.

So Croatian prefers:

• da je žirafa smiješna

not:

• da žirafa je smiješna

This is a very important word-order rule in Croatian.

Because both adjectives agree with feminine singular nouns:

• žirafa is feminine, so smiješna
• zebra is feminine, so ljepša

Croatian adjectives change their form to match the noun they describe.

Dictionary forms are often given in the masculine:

• smiješan = funny
• lijep = beautiful

But here the feminine forms are needed:

• smiješna
• ljepša

Ljepša is the comparative form of lijep / lijepa / lijepo = beautiful.

So:

• lijepa = beautiful
• ljepša = more beautiful / prettier

This adjective has a stem change, so it is not formed in a perfectly transparent way. It is best learned as:

• lijep → ljepši
• feminine: lijepa → ljepša

A often connects two ideas that are being contrasted or set against each other.

Here it means something like:

• while
• whereas
• and as for

So the sentence has this feeling:

• the giraffe is funny, whereas the zebra is prettier

It is weaker and more neutral than ali = but.

Because Croatian often leaves out a repeated je when it is easy to understand from the context.

The full version would be:

• Moja kći kaže da je žirafa smiješna, a zebra je ljepša od svih drugih životinja.

The shorter version in your sentence is natural and avoids repetition.

Because Croatian normally uses od after a comparative adjective.

So:

• ljepša od zebre = prettier than the zebra
• ljepša od svih drugih životinja = prettier than all the other animals

Here od corresponds to English than.

Because after comparative od, Croatian uses the genitive.

So the whole phrase svih drugih životinja is in the genitive plural:

• svih = genitive plural of svi = all
• drugih = genitive plural of drugi = other
• životinja = genitive plural of životinja = animals

So literally it is something like:

• than of all other animals

but in natural English we simply say:

• than all other animals

Because drugih = other makes the comparison logical and precise.

If you said only svih životinja, that could sound as if the zebra were being compared with a group that includes the zebra itself. By saying all other animals, Croatian makes it clear that the zebra is excluded from the comparison set.

No. This is grammatical gender, not biological sex.

As nouns, žirafa and zebra are grammatically feminine words, so adjectives agreeing with them must also be feminine:

• žirafa je smiješna
• zebra je ljepša

That is true even if you are talking about a male animal.

A few useful pronunciation notes:

• ž in žirafa sounds like the s in measure
• š in ljepša sounds like English sh
• lj is a single Croatian sound, not a normal English l + j
• ć in kći is a soft consonant sound that English does not have exactly

For many learners, kći is one of the hardest words to pronounce naturally, so it is completely normal if it feels difficult at first.