Šefica je rekla da ćemo, ako završimo projekt na vrijeme, sutra otići ranije kući.

This is a normal Croatian past tense form.

• je = is/has form of biti in the 3rd person singular
• rekla = past participle of reći, in the feminine singular

Together, je rekla means said.
The participle agrees with the subject, so because šefica is feminine, it must be rekla. With a male boss, it would be šef je rekao.

Da introduces a subordinate clause and here means that:

• Šefica je rekla da... = The boss said that...

This is extremely common in Croatian after verbs like reći (to say), misliti (to think), znati (to know), and similar verbs.

This is the Croatian future tense.

• ćemo = we will
• otići = to leave / go

Together, ćemo otići means we will leave / go.

Croatian often forms the future with the auxiliary ću, ćeš, će, ćemo, ćete, će plus an infinitive. Because ćemo is a clitic, it tends to appear near the beginning of its clause, while the infinitive can appear later. So da ćemo ... otići is normal.

You may also see other word orders, such as otići ćemo, depending on the sentence structure.

After ako meaning if, Croatian normally uses the present tense to talk about a future condition, just like English does in if we finish.

So:

• ako završimo projekt = if we finish the project

Here završimo is the present-tense form of the perfective verb završiti. Even though it is a present form, the meaning is future because of the if clause and the overall context.

Using ako ćemo završiti would usually sound unnatural here.

Projekt is in the accusative singular because it is the direct object of završimo.

The reason it looks the same as the nominative is that many masculine inanimate nouns have identical nominative and accusative singular forms.

So:

• nominative: projekt
• accusative: projekt

That is completely normal.

Na vrijeme is a fixed expression meaning on time or in time, depending on context. In this sentence it means finishing by the expected deadline, so on time is the most natural English translation.

It is best learned as a whole phrase:

• doći na vrijeme = to arrive on time
• završiti na vrijeme = to finish on time

That part is an inserted conditional clause:

• ako završimo projekt na vrijeme = if we finish the project on time

Because it is inserted into the middle of the main clause, Croatian sets it off with commas on both sides.

The same sentence could also be rearranged, for example:

• Ako završimo projekt na vrijeme, sutra ćemo otići ranije kući.

In that version, the conditional clause comes first, so only one comma is needed after it.

Ranije means earlier. It is the comparative form of rano (early).

So otići ranije kući means to go home earlier or to leave for home earlier than usual / earlier than expected.

Croatian often uses comparatives without stating the exact comparison, as long as it is understood from context.

Kući means home in the sense of to home / homeward after a verb of motion.

So:

• ići kući = to go home
• otići kući = to leave for home / go home

By contrast:

• kuća = house as a basic dictionary form
• kod kuće = at home

So kući is the correct form here because the sentence involves movement.

Yes, Croatian word order is fairly flexible, but not completely free. This sentence could be rearranged in several natural ways, for example:

• Šefica je rekla da ćemo sutra, ako završimo projekt na vrijeme, otići ranije kući.
• Ako završimo projekt na vrijeme, šefica je rekla da ćemo sutra otići ranije kući.

The exact order can change the emphasis a little, but the basic meaning stays the same.

What usually matters most is keeping the clitics, such as je and ćemo, in acceptable positions. That is why Croatian word order feels flexible in some places but strict in others.