Ostat ćemo prijatelji zauvijek.

The basic verb is ostati. In standard Croatian, when a future-tense auxiliary like ćemo comes after an infinitive ending in -ti, the final -i is dropped:

ostati + ćemo → ostat ćemo

So ostat ćemo is the standard form here.

You can also put the auxiliary before the infinitive:

Mi ćemo ostati prijatelji zauvijek.

But ostati ćemo is generally not considered standard.

Ćemo means we will. It is the 1st person plural future auxiliary, related historically to the verb htjeti.

So:

• ostat ćemo = we will remain / we will stay
• ćemo ostati = also we will remain / we will stay

In this sentence, ćemo is what makes the verb future tense.

Croatian often leaves subject pronouns out because the verb form already tells you who the subject is.

Here, ćemo already shows we, so mi is not necessary.

That is why:

• Ostat ćemo prijatelji zauvijek. = natural
• Mi ćemo ostati prijatelji zauvijek. = also correct, but more explicit or emphatic

English usually needs we, but Croatian often does not.

Prijatelji is the nominative plural form of prijatelj and it matches the subject we.

It is not a direct object here. It is a predicate complement: it tells you what we will remain.

Compare:

• Oni su prijatelji. = They are friends.
• Ostat ćemo prijatelji. = We will remain friends.

So prijatelji is used because it describes the subject, not because something is being acted on.

Not in this sentence.

• prijatelje is accusative plural
• prijateljima is dative/instrumental plural
• prijatelji is nominative plural

After ostati in this kind of meaning, Croatian uses the form that describes the subject, so prijatelji is the right choice.

In Croatian, the masculine plural form is normally used for a mixed group or for a group whose gender is not specified.

So:

• prijatelji = male group, mixed group, or unspecified group
• prijateljice = all-female group

If two women are speaking, they would usually say:

Ostat ćemo prijateljice zauvijek.

Zauvijek is an adverb meaning forever.

It can move around somewhat, because Croatian word order is flexible. For example:

• Ostat ćemo prijatelji zauvijek.
• Zauvijek ćemo ostati prijatelji.
• Ostat ćemo zauvijek prijatelji.

All of these are understandable. The original version sounds natural and neutral.

Yes, and it is very close in meaning, but there is a small nuance.

• Bit ćemo prijatelji zauvijek. = We will be friends forever.
• Ostat ćemo prijatelji zauvijek. = We will remain friends forever.

Ostat ćemo emphasizes continuing to be friends, even as time passes or circumstances change. That is often why ostati is chosen.

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

• ostati is perfective
• ostajati is imperfective

In this sentence, ostati is the natural choice because the idea is a future result or continuing state seen as a whole: we will remain friends.

Ostajati would usually suggest repeated or ongoing action in a different sense, not the simple future statement used here.

A rough pronunciation guide is:

Ostat ćemo prijatelji zauvijek
≈ OH-stat CHYE-mo pree-YAH-te-lyi ZAH-oo-vyek

A few useful details:

• ć in ćemo is a soft sound, not the same as č
• lj in prijatelji is like a softened ly sound
• ije in zauvijek is pronounced clearly, not reduced the way English often reduces vowels

A more careful approximation is:

OH-stat chyemo pree-YAH-telyi zah-OO-vyek

Because ćemo is a clitic-like auxiliary form and normally does not stand at the very beginning of a sentence.

That is why Croatian prefers:

• Ostat ćemo prijatelji zauvijek.
• Mi ćemo ostati prijatelji zauvijek.

But not normally:

• Ćemo ostati prijatelji zauvijek.

So the sentence either starts with another word, or the main verb comes first in the shortened future form.