Kad imam temperaturu, nemam apetit.

Croatian often drops subject pronouns when they are not needed, because the verb ending already tells you who the subject is.

• imam = I have
• nemam = I don’t have

So ja is understood automatically.
You would add ja only for emphasis, contrast, or clarity:

• Kad ja imam temperaturu, nemam apetit, ali on ga ima.
  = When I have a fever, I don’t have an appetite, but he does.

Here kad means when.

Kad and kada both mean when, and both are correct. The difference is mostly one of style:

• kad = shorter, very common, more everyday
• kada = slightly more formal or more neutral in careful writing

So:

• Kad imam temperaturu, nemam apetit.
• Kada imam temperaturu, nemam apetit.

Both are natural.

Because kad means when, while ako means if.

This sentence describes something that happens as a regular fact or expected situation:

• Kad imam temperaturu... = When/whenever I have a fever...

If you said:

• Ako imam temperaturu...

that would sound more hypothetical:

• If I have a fever...

So kad is the better choice for a general statement like this.

It normally sounds like a general truth or habitual situation:

• Whenever I have a fever, I don’t have an appetite.

That is because both verbs are in the present tense:

• imam
• nemam

In Croatian, present tense is often used for things that happen regularly or are generally true.

Because the sentence starts with a subordinate clause introduced by kad:

• Kad imam temperaturu = subordinate clause
• nemam apetit = main clause

The comma marks the boundary between those two parts. In English, you also often use a comma after an introductory when-clause:

• When I have a fever, I don’t have an appetite.

Because temperatura is the direct object of imam, so it goes into the accusative case.

The dictionary form is:

• temperatura = nominative singular

But after imati (to have), you need the accusative:

• imam temperaturu

For many feminine nouns ending in -a, the accusative singular ends in -u:

• knjiga → knjigu
• ideja → ideju
• temperatura → temperaturu

Literally, temperatura means temperature, but in this kind of everyday medical context, imam temperaturu means I have a fever / I have a temperature.

So although the literal word is temperature, the practical meaning here is fever or raised body temperature.

Because the standard negative form of imati is written together:

• imam = I have
• nemam = I do not have

This is something you simply learn as the normal form. Croatian often writes ne separately with verbs, but some negative forms are commonly fused in standard language, and nemam is one of them.

So:

• nemam apetit = correct
• ne imam apetit = not correct

It does have a case here: it is also in the accusative, because it is the object of nemam.

The reason it looks unchanged is that apetit is a masculine inanimate noun, and for many such nouns, the accusative singular is identical to the nominative singular.

So:

• nominative: apetit
• accusative: apetit

That is why you do not see a different ending.

Yes, you may hear that too.

There are two possibilities:

• nemam apetit
• nemam apetita

Both can occur.
Very roughly:

• nemam apetit is straightforward and common
• nemam apetita uses the genitive, which can sound a bit more indefinite or stylistically different

For a learner, nemam apetit is perfectly good and natural.

Because Croatian does not have articles like English a/an/the.

So Croatian simply says:

• apetit
• temperaturu

and the context tells you whether English would use a, an, the, or no article at all.

That means one Croatian noun form can correspond to several English possibilities, depending on context.

Yes, you can. That is also natural.

• Kad imam temperaturu, nemam apetit.
• Nemam apetit kad imam temperaturu.

The core meaning is the same. The difference is mainly focus:

• starting with Kad imam temperaturu... puts the time/situation first
• starting with Nemam apetit... puts the main point first

Croatian word order is more flexible than English, though not completely free.