Kad završim ovaj zadatak, poslat ću ga učiteljici.

Yes. Kad and kada both mean when.

• kad is the shorter, very common form
• kada is a little fuller and can sound slightly more formal or emphatic in some contexts

In this sentence, Kad završim ovaj zadatak... is completely natural.

This is a very common Croatian pattern.

After words like kad meaning when, Croatian often uses the present tense of a perfective verb to talk about a future completed action.

So:

• Kad završim ovaj zadatak = When I finish this task
• literally it looks like When I finish/am-finished this task
• but in natural English, it is translated as future time

This is normal in Croatian. English does something a bit similar too: we say When I finish this task, I’ll send it, not When I will finish this task.

Završim is:

• 1st person singular
• present tense
• of the verb završiti = to finish

So it means I finish or, in this kind of sentence, when I finish.

The ending -im is typical for many verbs in this conjugation.

Because ovaj zadatak is the direct object of završim.

• ovaj = this
• zadatak = task / assignment

Here, zadatak is a masculine inanimate noun. In Croatian, the accusative singular of masculine inanimate nouns is usually the same as the nominative singular.

So:

• nominative: ovaj zadatak
• accusative: ovaj zadatak

That is why the form does not change here.

Croatian forms the simple future, often called future I, with:

• the infinitive of the verb
• plus a short form of htjeti = to want, which functions as a future auxiliary

So the full idea is:

• poslati ću → in standard spelling this becomes poslat ću

When the infinitive comes before the auxiliary ću, the final -i of the infinitive is usually dropped in writing:

• poslati + ću → poslat ću
• raditi + ću → radit ću
• pisati + ću → pisat ću

So poslat ću means I will send.

Yes.

Both patterns are possible:

• Poslat ću ga učiteljici
• Ja ću ga poslati učiteljici
• Ću ga poslati is not normally used by itself at the beginning without something before the clitic

A very important point: ću is a clitic, so it usually does not stand in the first position of a clause.

That is why:

• Poslat ću ga... is good
• Ja ću ga poslati... is good
• Ću poslati ga... is not the normal word order

Also note:

• if the infinitive comes first: poslat ću
• if ću comes before the infinitive: ću poslati

Ga is the short pronoun meaning him or it in the accusative singular.

Here it refers back to zadatak, which is masculine singular, so:

• zadatak = task
• ga = it

So:

• poslat ću ga = I will send it

Croatian often uses these short object pronouns instead of repeating the noun.

Because Croatian short pronouns and short auxiliary forms follow special clitic order rules.

In poslat ću ga:

• ću is the future auxiliary clitic
• ga is the object clitic

These short unstressed words tend to cluster together in a fixed order. In this sentence, ću ga is the natural sequence.

So:

• poslat ću ga = natural
• poslat ga ću = not natural
• ga ću poslat may appear in marked or special contexts, but it is not the basic form learners should copy first

Because učiteljici is in the dative case, which is used for the recipient after verbs like send.

You are sending something to the teacher, so Croatian uses the dative:

• base form: učiteljica = teacher (female)
• dative singular: učiteljici = to the teacher

So:

• poslat ću ga učiteljici = I will send it to the teacher

If the teacher were male, you would have:

• učitelj → učitelju

Yes, it matters grammatically.

Učiteljica means a female teacher. If the teacher is a woman, this is the correct noun. Croatian marks gender clearly in many nouns.

Compare:

• učitelj = male teacher
• učiteljica = female teacher

Because the noun is feminine, its dative singular is:

• učiteljici

So the gender affects the noun form.

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

• slati = to be sending / to send repeatedly / to send in general → imperfective
• poslati = to send once / to send successfully as a completed action → perfective

In this sentence, poslati is used because the speaker means one completed future action:

• finish the task
• send it

So poslat ću ga is the natural choice.

Because Kad završim ovaj zadatak is a subordinate time clause placed before the main clause.

Croatian normally separates that clause with a comma:

• Kad završim ovaj zadatak, poslat ću ga učiteljici.

This is similar to English:

• When I finish this task, I’ll send it to the teacher.

If the main clause came first, the punctuation pattern could differ depending on style, but in this sentence the comma is expected.

Yes, Croatian word order is fairly flexible, but not completely free.

Possible natural versions include:

• Kad završim ovaj zadatak, poslat ću ga učiteljici.
• Kad završim ovaj zadatak, ja ću ga poslati učiteljici.
• Kad završim ovaj zadatak, učiteljici ću ga poslati.

These all mean roughly the same thing, but the emphasis changes slightly.

The version you were given is a very neutral, natural one, so it is a good model to learn first.