Doći ću čim završim posao.

Because ću is a clitic in Croatian. Clitics usually do not stand in first position in a clause.

So:

• Doći ću = correct
• Ja ću doći = also correct
• Sutra ću doći = also correct
• Ću doći = not standard at the beginning of a sentence

In other words, if nothing comes before ću, Croatian often puts the infinitive first: Doći ću.

A useful extra note: with many verbs ending in -ti, the final -i is often dropped before ću:

• raditi → radit ću
• pisati → pisat ću

But doći ends in -ći, so it stays doći ću.

Yes. That is grammatically correct.

The difference is mostly about emphasis:

• Doći ću čim završim posao. = neutral, natural
• Ja ću doći čim završim posao. = emphasizes I
  (for example, if you want to contrast yourself with someone else)

Croatian often leaves out subject pronouns like ja unless they are needed for emphasis or clarity.

This is very common in Croatian. After time words like čim (as soon as), Croatian usually uses the present form, not the future.

So Croatian says:

• čim završim posao = as soon as I finish work

not:

• čim ću završiti posao = not natural here

Even though the action is in the future, the clause after čim normally uses the present form.

Because Croatian is a pro-drop language. The verb ending already shows who the subject is.

Here:

• završim = I finish

The ending -im tells you it is 1st person singular.

So Croatian does not need to say ja unless you want emphasis:

• čim završim posao = as soon as I finish work
• čim ja završim posao = as soon as I finish work

This is about aspect, which is very important in Croatian.

• završiti → perfective → to finish, to complete
• završavati / završavam → imperfective → to be finishing, to finish repeatedly / in progress

In this sentence, the idea is a completed action:

• first I finish
• then I come

So Croatian uses the perfective verb: završim.

Using završavam would change the meaning and sound wrong here, because čim usually points to the moment when one action is completed.

Here čim means as soon as.

It introduces a time clause and shows that the second action happens immediately after the first one.

So:

• Doći ću čim završim posao. = I’ll come as soon as I finish work.

This is slightly more immediate than kad:

• kad završim posao = when I finish work
• čim završim posao = as soon as I finish work

Both can be correct, but čim stresses that there is little or no delay.

Posao is in the accusative singular here because it is the direct object of završim.

You are finishing what?
→ posao

A useful point: posao is a masculine inanimate noun, and in the singular its nominative and accusative forms are the same:

• nominative: posao
• accusative: posao

So the form does not change, even though the case is accusative.

It can mean either, depending on context.

In this sentence, English would most naturally say:

• I’ll come as soon as I finish work

But posao can also mean:

• job
• task
• piece of work

So the exact nuance depends on the situation. If someone is speaking about their working day, work is the best translation. If they mean a specific task, job or task may fit better.

This sentence has both sounds:

• čim has č
• doći and ću have ć

A rough guide:

• č = like ch in church
• ć = a softer sound, somewhere between English t and ch; many learners approximate it as a soft ty/ch sound

So roughly:

• čim ≈ cheem
• doći ≈ DO-chee, but with a softer ch
• ću ≈ tyoo or soft chyoo, depending on how close you want to get

English does not have a perfect match for ć, so approximation is normal at first.