Ako mi ponestane vremena, završit ću zadatak sutra.

No. Mi here is the unstressed dative form of ja, so it means to me / for me, not my.

In this sentence, it marks the person affected by the situation:

• Ako mi ponestane vremena = If I run short of time
• literally, something like if time becomes insufficient to me

Compare:

• moje vrijeme = my time
• mi ponestane vremena = I run out of time / time runs short for me

Yes, but the meaning becomes less personal.

• Ako mi ponestane vremena = If I run short of time
• Ako ponestane vremena = If time runs short / if there isn’t enough time

So mi makes it clear that the shortage of time affects me, the speaker.

Ponestane comes from the verb ponestati, which means to run short of, to start lacking, or to run out of something.

It is often used with things like:

• vremena = time
• novca = money
• strpljenja = patience

So:

• ponestane mi vremena = I run short of time
• ponestane mi novca = I run short of money

It suggests that there was some amount available, but then it became insufficient.

Because Croatian structures this idea differently from English.

The person affected is shown by mi in the dative, while the verb ponestati is commonly used in 3rd person singular. The thing that is lacking appears in the genitive.

So Croatian does not literally say I run out time. It uses a structure more like:

• to me runs-short of time

That is why ponestane is not in a 1st person form.

Because ponestati normally takes the thing that is lacking in the genitive case.

The noun is:

• vrijeme = nominative singular
• vremena = genitive singular

So after ponestane, you say:

• ponestane vremena
• ponestane novca
• ponestane strpljenja

This is a very common Croatian pattern with verbs and expressions of lack.

Because in Croatian, after ako for a real future condition, you normally use the present tense, not the future tense.

So Croatian says:

• Ako mi ponestane vremena, završit ću zadatak sutra.

not standardly:

• Ako će mi ponestati vremena...

This is very similar to English in a way:

• If I have time, I’ll do it
• not If I will have time...

In Croatian, this present form often has future meaning in conditional clauses.

This is the standard way of writing the future tense when the infinitive comes before ću.

Two common patterns are:

• Ja ću završiti zadatak.
• Završit ću zadatak.

When the infinitive stands directly before the clitic ću, standard Croatian shortens završiti to završit:

• završit ću

So završiti ću is not the standard written form.

Because zadatak is the direct object of završiti, so it is in the accusative case.

The useful point here is that for many masculine inanimate nouns, the accusative singular looks the same as the nominative singular.

So:

• nominative: zadatak
• accusative: zadatak

Even though the form does not change, the case is still accusative because of its role in the sentence.

Because the sentence begins with a subordinate ako clause:

• Ako mi ponestane vremena = dependent clause
• završit ću zadatak sutra = main clause

When the if-clause comes first, Croatian puts a comma before the main clause.

Yes, Croatian word order is fairly flexible, and sutra can move.

The original sentence is natural:

• Ako mi ponestane vremena, završit ću zadatak sutra.

But you could also say:

• Ako mi ponestane vremena, sutra ću završiti zadatak.
• Ako mi ponestane vremena, zadatak ću završiti sutra.

The meaning stays very similar, but the emphasis changes slightly.

• Final sutra can give a natural end-focus to tomorrow
• Earlier sutra may highlight the time more strongly

Yes, aspect matters a lot.

• ponestati is perfective
• završiti is perfective

That fits this sentence because it describes:

1. a single possible future event: time runs short
2. a single completed future action: I will finish the task

Perfective verbs are very common when Croatian talks about one whole completed event.

If you used an imperfective verb instead, the meaning would shift toward an ongoing process, repeated action, or incomplete action, which would sound less natural here.

The nuance is different.

• nemam vremena = I don’t have time
• ne budem imao vremena = I won’t have time
• ponestane mi vremena = I run short of time

So ponestane mi vremena suggests that there was some time available, but it becomes insufficient. It sounds more like I start running out of time than simply I don’t have time.

That makes it a good choice in this sentence, because it describes a situation that may happen while you are working.