Želim da ostanemo prijatelji.

Because the sentence has two different grammatical subjects:

• želim = I want
• ostanemo = we stay/remain

In Croatian, when the subject of the second action is different from the subject of the first verb, a da + present-tense clause is very common:

• Želim da ostanemo prijatelji. = I want us to remain friends.

If the subject were the same, Croatian often uses the infinitive:

• Želim ostati ovdje. = I want to stay here.

So here, da ostanemo is the natural choice because I am wanting, but we are the ones remaining friends.

Ostanemo comes from the verb ostati, which means to stay or to remain.

Here it is:

• 1st person plural = we
• in a da-clause
• expressing something wanted or desired

So da ostanemo means something like:

• that we remain
• for us to stay

Even though the form looks like present tense, after da it often refers to something desired, intended, or future-oriented, not literally a present action happening right now.

Because prijatelji is a predicate noun after ostati.

In this sentence, friends describes what we are or remain. Croatian normally uses the nominative for that:

• ostanemo prijatelji = we remain friends

So:

• prijatelji = nominative plural
• prijatelje = accusative plural

The accusative would be wrong here, because friends is not a direct object. It is describing the subject we.

Croatian often drops subject pronouns when they are already clear from the verb ending.

Here:

• ostanemo already tells you the subject is we

So mi is unnecessary unless you want emphasis:

• Želim da ostanemo prijatelji. = neutral, normal
• Želim da mi ostanemo prijatelji. = more emphasis on we

This is very common in Croatian.

Ostati is perfective.

That matters because perfective verbs in Croatian usually refer to a completed result or a single outcome, not an ongoing process. Here the idea is:

• to remain / end up continuing as friends

So ostanemo focuses on the result or state being maintained.

The imperfective partner is ostajati, but that would usually suggest repeated or ongoing action in a different way and would not sound natural here for this meaning.

So:

• Želim da ostanemo prijatelji. = I want us to remain friends

This is the normal choice.

Yes, but it is not exactly the same.

• Želim da budemo prijatelji. = I want us to be friends
• Želim da ostanemo prijatelji. = I want us to remain friends

The sentence with ostanemo implies that the two people are already friends, and the speaker wants that to continue.

The sentence with budemo is more general and can mean either:

• the speaker wants a friendship to exist, or
• wants the friendship to continue, depending on context

So ostanemo is more specific.

Yes, it is natural and clear.

It is a normal way to say:

• I want us to stay friends
• I want us to remain friends

That said, in very formal prescriptive grammar, some people prefer infinitive constructions where possible, but in everyday Croatian, da + present is extremely common and fully natural.

So for a learner, this is a good, useful sentence.

Because želim means I want, and that wanting exists now.

The sentence does not mean the remaining-friends action is happening right now in a literal present-time sense. Instead, it means:

• Right now, I have the wish/desire that we remain friends.

So the main verb is present because the desire is present, while the da clause expresses what the speaker wants to happen or continue.

Yes, Croatian word order is flexible, though the original version is the most neutral:

• Želim da ostanemo prijatelji.

You could also hear:

• Da ostanemo prijatelji, to želim.
  This is much more marked and stylistic.

Or with emphasis:

• Ja želim da ostanemo prijatelji.
  Emphasizes I
• Želim da mi ostanemo prijatelji.
  Emphasizes we

So the usual, most natural order is the one you were given.

It can, depending on context.

By itself, Želim da ostanemo prijatelji is grammatically neutral. It simply means I want us to remain friends.

But in real life, it is often used in emotionally loaded situations, for example:

• after an argument
• after a romantic breakup
• when trying to preserve a relationship in a non-romantic form

So the emotional tone comes mostly from the situation, not from the grammar itself.